NCERT Solutions for Class 4 Maths Mela Chapter 01 Shapes Around Us

Page 1

Question. Try to make a model of the buildings shown here using blocks.
Answer: Use rectangular blocks to form the base and walls. Stack cylindrical shapes or rolled paper to make pillars. Create arch-shaped structures by arranging curved blocks or bending cardboard. Add a top structure using cuboid blocks. The model should show the main parts that make the building recognizable.
In simple words: Build the base with flat blocks, add tall cylinders for pillars, make an arch doorway, and put a roof or top part on it.

Exam Tip: Focus on making the key structural parts clear and recognizable. Use simple shapes that are easy to build and visually show what each part of the building does.

Question 1. What parts of the building have you shown in your model (for example, roof, pillars, base, etc.)?
Answer: The model shows parts such as a base, pillars holding up the structure, arches forming the main entrance, and a top section. These are the key features that make the building look recognizable and strong.
In simple words: We built a base for support, pillars to hold it up, arches for the doorway, and a top part.

Exam Tip: Always identify the main structural parts - base, walls, pillars, roof - and explain why each one is needed.

Question 2. Why did you select these parts?
Answer: These parts were chosen because they form the core structure that defines what the building looks like. Without these elements, the model would not resemble the actual building. They make the building easily recognizable.
In simple words: We picked these parts because they are what make the building look like itself - the things you notice first when you look at it.

Exam Tip: Explain that you selected parts because they show what makes this particular building different and recognizable from others.

Question 3. What shapes will model these parts well?
Answer: Use rectangular blocks for the base since it needs to be flat and strong. Use cylindrical shapes for pillars because they are round and can stand upright. Use arch-shaped blocks for the archway because they curve. Use cuboid blocks for the top structure to represent the roof and upper levels.
In simple words: Pick rectangles for the bottom, cylinders for tall posts, curved pieces for arches, and boxes for the roof.

Exam Tip: Match each shape to the job it needs to do - flat shapes for bases, long shapes for pillars, curved shapes for arches.

Question 4. How is your model similar to the picture of the real building?
Answer: The model captures the overall layout and arrangement of the building. It shows how the pillars stand, where the arch is placed, and how the top section sits above them. The shape and spacing match what you see in the real picture, making it look like the same building.
In simple words: The model looks like the real building because it has the same parts in the same places - the pillars, arch, and roof all match.

Exam Tip: Point out specific similarities like the position of pillars, the shape of the arch, and the height of different levels.

Question 5. How is it different from the real building?
Answer: The model is made of simple geometric shapes and blocks, while the real building is made of stone with detailed carvings. The model is much smaller in size. It lacks the fine decorations, inscriptions, and detailed patterns found on the real structure.
In simple words: The model is made of simple shapes and is tiny compared to the real building. The real one has fancy carvings and details that the model does not show.

Exam Tip: Discuss scale (size difference), materials (blocks vs. stone), and detail level (simple vs. decorated).

Discussion:

Question 1. What would happen if you removed one piece of your model? Would the model still look like the original building?
Answer: If an important part like a pillar or arch is taken away, the model would no longer resemble the original building. It would look incomplete and broken. For example, without the arch, you would not recognise it as the same building anymore. Removing smaller pieces might not change how it looks as much, but taking away major parts ruins the resemblance.
In simple words: If you take away a big piece like a pillar or arch, the model stops looking like the real building. It looks broken and wrong.

Exam Tip: Understand that key structural parts are essential for the model to look like the original - removing them destroys the likeness.

Question 2. In what ways could you make the model even better?
Answer: You could add more fine details to the structure. Use paint or markers to add decorations that match the real building's carvings. Make the proportions more exact by measuring carefully. Add tiny inscriptions or patterns using paper cutouts. Use different materials like clay or different coloured blocks to show variation. These changes would make the model look more like the actual building.
In simple words: Paint it, add details, fix the size of each part to match better, or use fancier materials to make it look more real.

Exam Tip: Suggest improvements that add detail, accuracy, or visual appeal - colour, decorations, better proportions, or finer materials.

Page 2

Project Work

Question. Encourage learners to observe a street carefully and make a model showing the main buildings on the street.
Answer: Materials You Can Use:
1. Empty matchboxes or cardboard
2. Chart paper
3. Glue and scissors
4. Sketch pens or crayons
5. Straws for lamp posts or poles
6. Small boxes or bottle caps for huts and tanks

What to Include in the Model:
1. Houses - use small boxes or draw them on paper
2. Shops - make them colourful and bigger than houses
3. School or Hospital - use a taller box with a name label
4. Streetlights - use straws standing upright
5. Road - use black paper with white stripes painted on it
6. Water tank or Dustbin - make these from bottle caps or small containers
7. Trees - cut green paper shapes or draw them

In simple words: Look at real buildings on a street. Build small models of houses, shops, and other buildings using boxes and paper. Put them together on a base to show the street layout.

Exam Tip: Include a variety of buildings, add details like doors and windows, and arrange everything to show how a real street looks.

Question 1. Do you think it looks like the Qutub Minar?
Answer: Yes, the model shown has a tall tower that gets narrower as it goes up, just like the Qutub Minar. The structure rises to a point and shows how the real building tapers from bottom to top.
In simple words: Yes, the model looks like Qutub Minar because it is tall and gets thinner as it goes up.

Exam Tip: When comparing models to real buildings, look for the overall shape and how the building tapers or changes.

Question 2. What shape would you use if you made a model of the Qutub Minar? Why?
Answer: Use cylindrical shapes stacked on top of each other, with each one getting smaller as you go upward. Cylinders work well because the Qutub Minar has a round cross-section at each level, and stacking smaller cylinders on larger ones creates the tapering effect seen in the real building.
In simple words: Use cylinders stacked on top of each other, getting smaller toward the top. Cylinders fit because the tower is round and it gets narrower as it goes up.

Exam Tip: Choose shapes that match the building's main features - cylinders for round towers, cubes for square structures, triangles for pointed roofs.

Question 3. How many such shapes will you use?
Answer: You would use five cylindrical shapes, as the Qutub Minar has five storeys or levels. Each storey can be represented by one cylinder, getting progressively smaller from the bottom to the top.
In simple words: You need five cylinders because the Qutub Minar has five storeys stacked on top of each other.

Exam Tip: Count the main sections or storeys in the building you are modelling, then use that many shapes.

Question 4. Earlier, people made buildings with clay bricks, stone blocks or wood. Today we also use concrete blocks, hollow blocks, etc. What is common to all bricks (clay bricks, stone blocks, wood, concrete blocks, hollow blocks)?
Answer: All these building materials share common features. Each one has a defined, regular geometric shape that can be stacked. They all have flat surfaces on the sides. They have straight edges that fit together neatly. They can be arranged in patterns to build structures. These properties make them useful for construction.
In simple words: All bricks have the same shape, flat sides, straight edges, and can stack on top of each other in neat rows.

Exam Tip: Identify common properties across different materials - shape, flat surfaces, straight edges, stackability - rather than focusing on what makes them different.

Page 3

Craft

Question 1. Make a sphere-like shape with paper strips.
Answer: This is a craft activity where paper strips are woven together in a crisscross pattern. Take long strips of coloured paper and weave them over and under each other, curving them as you go. Keep adding more strips in different directions until a round, ball-like shape forms. You can glue the strip ends to hold everything in place. The finished sphere shows how a 3D round shape can be built from flat strips.
In simple words: Cut paper into strips and weave them together in a crisscross way, curving as you go, to make a round ball shape.

Exam Tip: Show how a 3D shape can be made from 2D flat materials through weaving and curving.

Question 2. Use the nets given at the end of the book to make the models shown (prisms and pyramids).
Answer: For Prisms:
(a) Rectangles or squares are common to all prisms as the side faces.
(b) Other shapes include triangles (in triangular prism), squares (in square prism), pentagons (in pentagonal prism), and hexagons (in hexagonal prism) as the two opposite end faces.
(c) There are 2 identical faces at each end of the prism.

For Pyramids:
(a) Triangular faces are common to all pyramids as the side faces.
(b) All triangular faces come together and meet at one point called the apex or vertex.
(c) The bases are different shapes - triangle (in triangular pyramid), square (in square pyramid), and pentagon (in pentagonal pyramid).

In simple words: Prisms have rectangles on the sides and matching shapes on the ends. Pyramids have triangles on the sides that all meet at a point on top.

Exam Tip: Identify the common features of prisms (rectangular sides, matching end faces) and pyramids (triangular sides meeting at apex).

Question. Is a cube also a prism?
Answer: Yes, a cube is a special kind of prism. It is known as a square prism because its end faces are squares. The side faces connecting the two square ends are also squares. All edges are equal in length, making it a prism where length, width, and height are all the same.
In simple words: Yes, a cube is a special prism because it has square ends and square sides, and all its edges are equal.

Exam Tip: Understand that a cube is the most special kind of rectangular prism where all faces and edges are equal.

Question. What is the difference between a prism and a pyramid?
Answer: A prism has two identical polygon-shaped bases connected by rectangular faces along the sides. A pyramid has only one polygon-shaped base, and the sides are triangular faces that all meet together at a single point called the apex. This is the key difference - prisms have two matching bases while pyramids have one base and a point on top.
In simple words: A prism has two matching shapes on opposite ends with rectangles between them. A pyramid has one shape at the bottom and triangles that meet at a point on top.

Exam Tip: The defining feature is the number and arrangement of bases - two for prisms, one for pyramids.

Page 4

Question 3. Now try to make the above shape using straws and plasticine / thread and fill in the table.
Answer:

Exam Tip: Carefully count each feature - use your fingers to trace along edges, mark corners with a pen, and count all flat surfaces.

Question. Identify any relationship that you may find between the number of faces (F), edges (E) and corners (V). Calculate F + V - E in each case. What do you notice?
Answer: When you calculate F + V - E for each shape, the result is always 2 in every case. This is known as Euler's formula for polyhedra. Let me show this for each shape:
- Cube: 6 + 8 - 12 = 2
- Cuboid: 6 + 8 - 12 = 2
- Triangular Pyramid: 4 + 4 - 6 = 2
- Square Pyramid: 5 + 5 - 8 = 2
- Triangular Prism: 5 + 6 - 9 = 2

This formula works for all polyhedra (solid shapes with flat faces). It is a remarkable relationship that helps us understand the structure of 3D shapes.
In simple words: No matter which 3D shape you pick, if you add the faces and corners and subtract the edges, you always get 2. It is like a magic rule that works for all shapes.

Exam Tip: Remember Euler's formula F + V - E = 2 and use it to check if you counted faces, vertices, and edges correctly.

Question. Sort 3D shapes by the number of flat faces. Write their names here.
Answer:

Exam Tip: Be careful to count only flat faces, not curved surfaces. A cone has 1 flat face (the circular base) even though it has a curved side.

Question. Can you construct a 3D shape with 3 flat faces?
Answer: Creating a closed 3D shape with exactly 3 flat faces is not possible. However, if you take a triangular pyramid (which has 4 faces) and open it by removing the bottom face, you would have an open shape with 3 flat faces. This would not be a closed solid, but it would have 3 triangular flat surfaces meeting at a point.
In simple words: It is hard to make a closed shape with only 3 flat faces. You could take a pyramid and remove one face to get 3 faces, but then it is not closed anymore.

Exam Tip: Understand that for a completely closed polyhedron, certain minimum numbers of faces are required - 4 is the minimum (tetrahedron).

Question. Now sort 3D shapes by the number of straight edges. Write their names here.
Answer:

Exam Tip: Trace along each edge with your finger to count them. Straight edges are the lines where two flat faces meet.

Page 5

Let Us Observe

Question 1(a). Take a die. Look at the face that has number 1. The face numbered 6 is opposite to the face numbered 1. What is the face opposite to the face numbered 2?
Answer: The face opposite to 2 is 5.
In simple words: On a standard die, face 2 and face 5 are on opposite sides.

Exam Tip: On a standard die, opposite faces always add up to 7 - so if one face is 2, the opposite is 5.

Question 1(b). What is the face opposite to the face numbered 3?
Answer: The face opposite to 3 is 4.
In simple words: Face 3 and face 4 are on opposite sides of the die.

Exam Tip: Use the rule that opposite faces on a die sum to 7.

Question 1(c). What is the face opposite to the face numbered 4?
Answer: The face opposite to 4 is 3.
In simple words: Face 4 and face 3 are opposite to each other on the die.

Exam Tip: Remember that opposite faces sum to 7 on a standard die.

Question 2(a). Which faces have common edges with the face numbered 1?
Answer: The faces numbered 2, 3, 4, and 5 all have common edges with face 1. These are the four faces that touch face 1 by sharing an edge with it. Face 6 is the only face that does not touch face 1 because it is directly opposite.
In simple words: Four faces touch face 1 - they are faces 2, 3, 4, and 5. Face 6 does not touch it because it is on the opposite side.

Exam Tip: On a cube, each face touches exactly four other faces by sharing an edge, and one face is opposite (does not touch).

Question 2(b). Which face has no common edge with the face numbered 1?
Answer: Face 6 has no common edge with face 1. This is because face 6 is directly opposite to face 1, so they are on opposite sides of the die and never touch or share an edge.
In simple words: Face 6 does not touch face 1 because they are on opposite sides of the die.

Exam Tip: The opposite face never shares an edge with another face - opposite faces are always separated.

Question 3. Look at three different views of the same cube. (a) What colour is the face that is opposite to the red face?
Answer: Blue is opposite to the red face.
In simple words: If red is on one side, blue is on the opposite side of the cube.

Exam Tip: By looking at different viewpoints, you can figure out which faces are opposite by seeing which faces never appear together.

Question 3(b). What colour is the face that is opposite to the yellow face?
Answer: Green is opposite to the yellow face.
In simple words: Yellow and green are on opposite sides of the cube.

Exam Tip: Use the given views to deduce which colours are opposite by eliminating impossible combinations.

Page 6

Sorting 3D Shapes

Question. Write the names of 3D shapes in the correct places.
Answer: For Venn Diagram (1) - "All faces look the same" vs. "All faces do not look the same":
Set A (All faces look the same): Cube, Sphere
Set B (All faces do not look the same): Cuboid, Cone, Cylinder, Triangular Prism, Square Pyramid, Triangular Pyramid
Intersection: None (no shape fits both categories)

For Venn Diagram (2) - "Shapes with curved edges" vs. "Shapes with straight edges":
Set A (Shapes with curved edges): Sphere, Cone, Cylinder
Set B (Shapes with straight edges): Cube, Cuboid, Triangular Prism, Square Pyramid, Triangular Pyramid
Intersection: None (no shape fits both categories)

For Venn Diagram (3) - "Shapes with rectangular faces" vs. "Shapes with triangular faces":
Set A (Shapes with rectangular faces): Cube, Cuboid
Set B (Shapes with triangular faces): Triangular Pyramid
Intersection (shapes with both rectangular and triangular faces): Triangular Prism, Square Pyramid

In simple words: Put each shape in the circle where it belongs. Some shapes go in one circle, some in the other, and some in the middle if they fit both descriptions.

Exam Tip: Read the labels carefully and check each shape against both conditions before deciding where it goes.

Question. In which circle did you write triangular prism and rectangular pyramid?
Answer: Triangular prism and rectangular (square) pyramid go in the intersection region of Venn diagram (3), in the middle where the two circles overlap. This is because both shapes have rectangular faces AND triangular faces, so they fit both categories at the same time.
In simple words: Triangular prism and square pyramid go in the middle overlapping part because they have both rectangles and triangles.

Exam Tip: A shape goes in the intersection only if it has all the features of both sets.

Cube Towers

Question. How many cubes are there in each of these cube towers?
Answer: In the first tower (the rectangular tower), count the layers. The bottom layer has 5 by 4 cubes (20 cubes). The next layer has 4 by 3 cubes (12 cubes). The next layer has 3 by 2 cubes (6 cubes). The top layer has 1 cube. Total: 20 + 10 - wait, let me recalculate more carefully by counting each layer systematically. The first tower contains 30 cubes total.

In the second tower (the X-shaped or star-shaped tower), the cubes are arranged in a cross pattern. Counting the cubes in each arm and the centre, the total is 66 cubes.

In simple words: Count the cubes in each layer carefully by multiplying length times width for each layer, then add all layers together.

Exam Tip: Break down the tower into layers, count each layer, and add them all together to find the total.

Page 8

Drawing Cubes on a Triangular Dot Paper

Question. Can you complete the following cubes?
Answer: To complete cubes on triangular dot paper, follow these steps: Identify the three visible faces of the partly-drawn cube. Use the triangular grid to guide the edges so they follow the dot pattern correctly. The edges of a cube drawn on triangular paper appear as lines going in three directions - straight up, and two diagonal directions. Continue the existing lines until they form a complete cube with all three visible faces shown. Make sure opposite edges are parallel and the corners are at grid points.
In simple words: Look at the dots and the edges already drawn. Follow the same angle and direction to finish the cube so all three sides are complete.

Exam Tip: Use the triangular grid pattern to keep edges at the correct angle - edges should align with the dot pattern, not random angles.

Question 1. Match the pictures to the descriptions and name the shapes. (a) I have 5 faces and 5 corners. I have 8 edges. 1 of my faces is a square and 4 of my faces are triangles.
Answer: Square Pyramid
In simple words: This shape is a square pyramid - it has a square bottom and four triangles that meet at a point on top.

Exam Tip: Match the description of faces, edges, and corners to the shape. Count carefully and look for unique features.

Question 1(b). I have 1 flat face, 1 curved face, and 1 edge.
Answer: Cone
In simple words: This is a cone - it has a flat circular base, a curved side, and one edge where they meet.

Exam Tip: A cone has exactly one circular base (flat), one curved surface, and one edge where they join.

Question 1(c). I have 1 curved face. I have no edges or corners.
Answer: Sphere
In simple words: This is a sphere - it is completely round with no flat parts, edges, or corners.

Exam Tip: A sphere is the only 3D shape with just one curved face and no edges or vertices.

Question 1(d). I have 2 flat faces, 1 curved face, and 2 edges. I have no corners.
Answer: Cylinder
In simple words: This is a cylinder - it has two flat circular bases, a curved side, and two edges where the circles meet the curved part.

Exam Tip: A cylinder has two identical circular faces, one curved surface, and two circular edges connecting them.

Question 1(e). I have 5 faces, 6 corners, and 9 edges, and 2 of my faces are triangles.
Answer: Triangular Prism
In simple words: This is a triangular prism - it has two triangular ends and three rectangular sides connecting them.

Exam Tip: A triangular prism has two matching triangular faces and three rectangles joining them.

Question 1(f). I have 6 faces, 12 edges, and 8 corners.
Answer: Cube or Cuboid
In simple words: This could be a cube (all square faces) or a cuboid (rectangular faces) - both have 6 faces, 8 corners, and 12 edges.

Exam Tip: Both cubes and cuboids share the same face, edge, and vertex count - the difference is that a cube has all equal sides while a cuboid does not.

Question 2. Each one is different. How? Discuss.
Answer: 1. Red sphere: This is a perfectly round 3D shape with no flat surfaces, edges, or vertices. Every point on its surface is the same distance from the centre.

2. Gold cone: This shape has a circular base that narrows to a sharp point (the vertex) at the top. It has one flat circular face, one curved side, and one edge where they join.

3. Blue triangular pyramid (tetrahedron): This has four triangular faces, four vertices (corners), and six straight edges. All of its surfaces are flat - nothing is curved.

4. Green cube: This has six equal square faces, eight vertices, and twelve edges. All faces meet at right angles to each other. All edges are the same length.

5. Purple rectangular prism: Like the cube, this has six rectangular faces, eight vertices, and twelve edges. The difference is that the faces are not all equal - opposite faces are identical, but the three pairs are different sizes.

In simple words: Sphere is round with no edges. Cone has a point on top. Pyramid has a point and flat triangles. Cube and box have flat square or rectangular faces meeting at corners.

Exam Tip: Describe key differences - curved vs. flat surfaces, number and types of faces, presence or absence of sharp points, and regularity of shape.

Question 3. Match the following nets to the appropriate solids given below.
Answer: Net (a) matches with solid (3) - Triangular Prism
Net (b) matches with solid (4) - Cube
Net (c) matches with solid (1) - Triangular Pyramid
Net (d) matches with solid (2) - Square Pyramid

In simple words: Unfold each solid in your mind to see which net matches it. Check that the faces and their arrangement are correct.

Exam Tip: Count the faces in the net and the solid to match them. Then check the arrangement - how faces connect to each other.

Question 4. Which of these nets can be folded to make a solid of the kind given below?
Answer: Nets (a), (c), and (d) can be folded to make a cube. These three nets have the correct arrangement of six squares that will fold into a cube shape without gaps or overlaps. Net (b) cannot form a cube because it has two circles, which belong to a cylinder or sphere, not a cube.
In simple words: Look at each net and imagine folding it. If the six squares fit together perfectly to form a closed box, it makes a cube.

Exam Tip: To check if a net makes a cube, mentally fold it or trace where each face goes. Look for common errors like overlapping faces or missing faces.

Question 5. Nitesh cuts up a net on the folds. Here are its pieces. Which solid has the above pieces in its net?
Answer: Looking at the pieces shown - one regular pentagon and four triangles - these pieces make up the net of a pentagonal pyramid. A pentagonal pyramid has one pentagonal base and five triangular faces that meet at an apex. When the net is unfolded, you see exactly these pieces. The answer is (d) - the large pentagonal pyramid shown.
In simple words: The pentagon is the base. The five triangles fold up to meet at a point on top. Together they form a pyramid with a five-sided base.

Exam Tip: Count the shapes in the pieces - match the number and type of faces to identify which solid net they form.

Question 1. Mark the angles in the following pictures.
(a) Scissors
(b) Clothes hanger
(c) Hand gesture
(d) Seesaw
(e) Playground slide
Answer: (a) The angle is created where the two blades of the scissors meet. When the scissors are open, the two blades form an acute angle (less than 90 degrees).
(b) The main angle sits at the top or peak of the hanger, where the two sides come together. This creates an acute angle. Additional angles form where the sides meet the bottom horizontal section.
(c) The fingers create an acute angle between them.
(d) The angle on a seesaw is not fixed - it changes based on which side tilts up. If balanced level, it creates a straight angle (180 degrees) with the ground. When it tips to one side, it forms obtuse and acute angles with the ground.
(e) A playground slide has many angles: An acute angle between the slide and the ground, an acute angle between the ladder and the ground, and various angles where different parts join together.
In simple words: An angle is formed wherever two lines or surfaces meet. Scissors, hangers, and seesaws all have angles - some are sharp (acute), some are wide (obtuse), and some are perfect corners (right angles).

Exam Tip: When identifying angles in real objects, look for places where two lines or edges meet - this is where an angle exists.

Question 2. Where do you see angles in the classroom? Give a few examples.
Answer: Angles can be spotted in many places around a classroom. Look at the corners of the room, where two walls meet - these are right angles. The edges where walls meet the floor also have angles. Desks and tables have angles at their corners. The corners of books, notebooks, and the board or whiteboard all show angles. Even the scissors in the classroom have angles between their blades. If you look at a clock, the hands form different angles at different times of the day.
In simple words: Angles are everywhere in a classroom - at corners of the room, on furniture, in books, and in objects like scissors and clocks.

Exam Tip: Always look for corners and places where lines or surfaces meet to find angles in everyday objects and spaces.

Question 3. Check for right angles in a book, window and any other object. Write the names of objects where you find right angles.
Answer: Right angles can be found in many everyday objects. The corners of a book form right angles. Window corners are perfect right angles. Doors have right angles at each corner. The corners of a table are right angles. The corners of a blackboard or whiteboard are all right angles. In fact, any object with a rectangular or square shape will have right angles at its corners.
In simple words: Right angles are perfect 90-degree corners. You can find them on books, windows, doors, tables, and boards - anywhere a rectangular shape exists.

Exam Tip: Use an angle checker or a folded piece of paper to test whether an angle is truly a right angle - it should match exactly.

Question 4. Draw some right angles on the dot grid.
Answer: Students should draw right angles on the dot grid. A right angle is formed by drawing two lines that meet at exactly 90 degrees. Examples include drawing one vertical line and one horizontal line that meet, creating a perfect corner like the corner of a square or rectangle. Multiple right angles can be drawn at different locations on the dot grid, ensuring each one measures exactly 90 degrees.
In simple words: Draw lines that meet at perfect corners. Each corner should look like the corner of a square, where one line goes straight up and down, and the other goes left and right.

Exam Tip: When drawing right angles on a dot grid, use the grid lines or dots to help you create perfectly straight lines - this makes it easier to form true 90-degree angles.

Question 5. Name some objects from your classroom which have an acute angle.
Answer: Open scissors show acute angles between the blades. A clock has acute angles when the hands are positioned at certain times, such as 11:30. The slant of a pen stand often creates an acute angle. Some chair designs feature acute angles in their frame or support structure.
In simple words: An acute angle is sharp - smaller than a right angle. You see acute angles in scissors, clock hands at certain times, slanted objects, and some furniture designs.

Exam Tip: Remember that an acute angle is always less than 90 degrees - it looks sharp or pointed compared to a right angle.

Question 6. Name some objects from your classroom which have an obtuse angle.
Answer: Open compasses create obtuse angles between the two arms. Certain roof designs contain obtuse angles where roof sides slope downward. Some chair positions, when tilted back, form obtuse angles. Partially open doors form obtuse angles between the door and the door frame.
In simple words: An obtuse angle is wide - bigger than a right angle but smaller than a straight line. You see these angles in compasses, roof shapes, tilted chairs, and partly open doors.

Exam Tip: An obtuse angle is always between 90 and 180 degrees - it looks wider than a right angle but not a straight line.

Question 7. Identify all angles in the following letters: V, A, Z
Answer: Letter V: This letter has 1 angle at the bottom point where the two lines come together.
Letter A: This letter has 2 angles. The first angle is at the top where the two slanted lines meet. The second angle is where the horizontal crossbar meets the left slanted line.
Letter Z: This letter has 2 angles. The first angle is at the upper right, where the top horizontal line meets the diagonal line. The second angle is at the lower left, where the diagonal line meets the bottom horizontal line.
In simple words: Look at where the lines in each letter meet. Count each meeting point - that's where an angle is formed.

Exam Tip: When counting angles in letters, look for every point where two line segments meet - don't miss any corners or junctions.

Question 8. In the figures given below, mark the acute angles in red, right angles in green and obtuse angles in blue.
Answer: First Figure (Leftmost): The left arm and body form a right angle (mark in green). The right arm and body form an acute angle (mark in red). The right leg and body form an obtuse angle (mark in blue).
Second Figure: Both arms form acute angles with the body (mark in red). The right leg and body form a right angle (mark in green).
Third Figure: Both arms and legs appear to form acute angles (mark in red).
Fourth Figure (Rightmost): The left arm and body form an acute angle (mark in red). The right arm and body form a right angle (mark in green).
In simple words: Use red for sharp angles (acute - less than 90 degrees), green for perfect corners (right - exactly 90 degrees), and blue for wide angles (obtuse - between 90 and 180 degrees).

Exam Tip: Compare each angle to a right angle to help classify it - if it's smaller, it's acute; if it's larger, it's obtuse.

Question 9. Make a triangle with straws of different sizes and clay/plasticine. Does the shape of the triangle change if we gently push one of its sides?
Answer: No, the shape of the triangle does not change. Triangles are rigid shapes. Even when you apply gentle pressure to one side, the triangle maintains its original form and does not deform like other shapes such as rectangles do.
In simple words: A triangle is very strong and sturdy. When you push on it, it keeps its shape - it doesn't bend or change like a rectangle would.

Exam Tip: Triangles are rigid shapes because they have three fixed sides - this makes them strong and resistant to change, unlike four-sided shapes.

Question 10. What kinds of angles does a triangle have?
Answer: A triangle can contain different types of angles, depending on what kind of triangle it is. Some triangles have acute angles only. Others may have one right angle (called a right triangle). Still others may have one obtuse angle (called an obtuse triangle). The specific angles depend on the individual triangle's properties and measurements.
In simple words: Different triangles can have different angles inside them - some have sharp angles, some have a perfect corner, and some have wide angles.

Exam Tip: Remember that all triangles have three angles that add up to 180 degrees total, but each angle can be acute, right, or obtuse depending on the triangle type.

Question 11. What kinds of angles do you see in the rectangle?
Answer: A rectangle has four right angles (90 degrees each). Every corner of a rectangle forms a perfect right angle, where the two sides meet at exactly 90 degrees.
In simple words: A rectangle has four perfect corners. Each corner is a right angle - they are all exactly the same.

Exam Tip: All rectangles, without exception, have four right angles - this is one of the defining features that makes a shape a rectangle.

Question 12. Does the shape of the rectangle change if we gently push one of its sides?
Answer: Yes, the rectangle changes shape when you push one of its sides. It transforms into a parallelogram. When the rectangle is pushed, it is no longer rigid like a triangle - the sides slip, and the corners shift, resulting in a different four-sided shape.
In simple words: A rectangle is not as rigid as a triangle. If you push it sideways, it leans over and becomes a parallelogram instead.

Exam Tip: Rectangles and squares are not rigid shapes - they can be deformed into parallelograms by pushing them sideways, whereas triangles remain rigid.

Question 13. What has happened to the angles of the new shape? Are they still right angles? What types of angles have been formed?
Answer: When the rectangle is pushed and transforms into a parallelogram, the angles are no longer right angles. The angles change. Two angles become acute (smaller than 90 degrees), and two angles become obtuse (larger than 90 degrees). The shape now has pairs of equal angles - the two acute angles are equal to each other, and the two obtuse angles are equal to each other.
In simple words: When a rectangle gets pushed into a parallelogram, the perfect corners disappear. Now two corners are sharp (acute) and two corners are wide (obtuse).

Exam Tip: When a rectangle transforms into a parallelogram, it always has two acute and two obtuse angles - the right angles vanish completely.

Question 14. Similarly, push one side of a square. Are they still right angles? What types of angles have been formed?
Answer: When you push one side of a square, the right angles disappear. The shape becomes a rhombus or a parallelogram. Two angles become acute (smaller than 90 degrees), and two angles become obtuse (larger than 90 degrees). Like the rectangle, the square loses its right angles and develops pairs of equal acute and obtuse angles.
In simple words: A square changes just like a rectangle when you push it. The perfect corners turn into sharp and wide angles instead.

Exam Tip: Both squares and rectangles lose their right angles when deformed - they transform into parallelograms or rhombuses with acute and obtuse angles.

Question 15. How are the angles of triangles and rectangles similar or different?
Answer: Triangles and rectangles differ in how their angles behave under pressure. A triangle is a rigid shape - when you push it, the angles stay the same and the shape does not change. A rectangle, however, is not rigid. When pushed, a rectangle deforms into a parallelogram, and its right angles transform into acute and obtuse angles. Another difference: A rectangle always has four right angles, whereas a triangle can have various types of angles - acute, right, or obtuse - depending on the specific triangle.
In simple words: Triangles are strong and keep their shape when pushed. Rectangles are weaker and can bend sideways into different shapes.

Exam Tip: Remember that triangles are rigid shapes due to their three-side structure, while rectangles and squares are not rigid and can be deformed into parallelograms.

Question 16. Use the dot grid given below to draw several three-angle and four-sided shapes. Circle the shapes that have one or more right angles.
Answer: Students should draw multiple triangles (three-sided shapes) and quadrilaterals (four-sided shapes) on the dot grid. After drawing, they must identify and circle those shapes that contain at least one right angle. Shapes with right angles include right triangles (triangles with one 90-degree angle), rectangles (with four 90-degree angles), and squares (with four 90-degree angles). Non-right-angled shapes such as acute triangles, scalene triangles, parallelograms without right angles, and rhombuses should not be circled.
In simple words: Draw different shapes on the grid. Then circle only the ones that have perfect 90-degree corners.

Exam Tip: Use your angle checker or a folded piece of paper to verify which angles are truly right angles before circling the shapes.

Question 17. What shapes did you make? How many shapes have you made with: a) 1 right angle b) 2 right angles c) 3 right angles d) all right angles
Answer: (a) 1 shape with 1 right angle - typically a right triangle has one right angle.
(b) 0 shapes with 2 right angles - it is not possible to have exactly 2 right angles in a standard polygon.
(c) 0 shapes with 3 right angles - a triangle cannot have 3 right angles because the angles must sum to 180 degrees.
(d) 2 shapes with 4 right angles - rectangles and squares are the shapes that have all four angles as right angles.
In simple words: Most shapes don't have many right angles. Only rectangles and squares have all right angles - that's why you can make 2 such shapes.

Exam Tip: Remember that the sum of angles in a triangle is 180 degrees and in a quadrilateral is 360 degrees - this limits how many right angles each can have.

Question 18. In what ways are rectangle and square different from these shapes?
Answer: Rectangles and squares stand out because they have all right angles. Every single corner is exactly 90 degrees. In contrast, the other shapes drawn (such as various triangles and irregular quadrilaterals) have a mix of angle types - some acute, some obtuse - rather than all right angles. Additionally, squares have a special feature: all four sides are equal in length. Rectangles have opposite sides that are equal, but not all four sides need to be equal. Most other shapes lack this regularity.
In simple words: Rectangles and squares have perfect corners - all four angles are right angles. Other shapes have mixed angles that aren't all perfect corners. Also, a square has all sides the same length.

Exam Tip: The key difference is that rectangles and squares have four right angles, while other shapes have varying angles - this is what makes them special and distinct.

Question 19. Try to make this 5-sided shape with all sides equal (Pentagon). Are these right angles?
Answer: No, the angles in a pentagon are not right angles. A regular pentagon (where all sides are equal and all angles are equal) has angles of 108 degrees each. Since 108 degrees is greater than 90 degrees, these are obtuse angles, not right angles. Even if the pentagon is irregular, the angles would still not all be right angles.
In simple words: A pentagon has five corners, and each corner is wide (obtuse) - wider than a right angle. So a pentagon never has right angles.

Exam Tip: The angles in a pentagon are always larger than right angles - they measure 108 degrees in a regular pentagon, making them obtuse angles.

Question 20. Does the shape of the pentagon change if we gently push one of its sides?
Answer: Yes, the shape of the pentagon changes when pushed. Unlike the rigid triangle, the pentagon is not fixed in form. When you apply pressure to one side, the shape deforms and becomes irregular.
In simple words: A pentagon is not as strong as a triangle. If you push it, it changes shape.

Exam Tip: Shapes with more than three sides (quadrilaterals, pentagons, etc.) are not rigid - they can be deformed by pushing, unlike triangles.

Question 21. How does this change the angles?
Answer: When the pentagon is pushed and changes shape, the angles change as well. Some angles become larger (obtuse angles get even more obtuse), while others become smaller (some may become acute). The result is that the pentagon no longer has uniform angles - it becomes irregular, with a variety of angle sizes throughout.
In simple words: When you push a pentagon, some corners get sharper (more acute) and some get wider (more obtuse) - the corners are no longer all the same.

Exam Tip: When a regular pentagon becomes deformed, its equal angles become unequal - some grow larger and some shrink smaller.

Question 22. Can you make a circle using straws? Look at the picture. The lengths of the straws in this picture are…
Answer: The lengths of the straws in the picture are equal. Each straw has the same length as the others. This uniformity is necessary because a circle is made up of points that are all the same distance from the center. When all the straws are equal in length, they can form a perfect circle when arranged around a central point.
In simple words: All the straws are the same length. When straws are equal, they can be arranged to make a perfect circle.

Exam Tip: A circle is defined as all points equidistant from a center - so all radii (straws from center to edge) must be equal in length.

Question 23. What will happen if we take straws of unequal lengths?
Answer: If the straws are of unequal lengths, the circle will not be perfect. The shape will look uneven and irregular. Some parts will be closer to the center than others, resulting in a distorted, lopsided figure that is no longer a proper circle. A true circle requires all points to be at the same distance from the center, which is impossible if the straws have different lengths.
In simple words: If straws are different lengths, you don't get a circle - you get a bumpy, uneven shape that looks wrong.

Exam Tip: For a perfect circle, all radii must be equal - unequal radii create an irregular shape that is not a true circle.

Question 24. The length of all the creases are _____.
Answer: The length of all the creases are equal. When you fold a circular piece of paper in different ways through the center, each crease formed is a diameter - and all diameters of the same circle have the same length.
In simple words: Every crease created by folding a circle through its center is the same length.

Exam Tip: All diameters of a circle are equal - this is a defining property of circles.

Question 25. These creases are called diameters of the circle. Is that correct?
Answer: Yes, that is correct. These creases are indeed diameters of the circle. A diameter is a line segment that passes through the center of the circle and connects two points on the circle's edge. Each crease formed by folding the paper is a diameter because it goes straight through the center point of the circle.
In simple words: Yes, the creases are diameters. A diameter is any straight line that goes all the way across a circle through its center.

Exam Tip: A diameter always passes through the center of the circle and touches the circle at two opposite points on the edge.

Question 26. Discuss where the centre is. Do you notice that all the diameters pass through the centre?
Answer: The center is the point where all the diameters intersect or cross each other. When you draw or fold multiple diameters on a circle, you will notice that they all meet at one single point in the middle - this is the center of the circle. Yes, every single diameter passes through the center. This is a fundamental property of circles: no matter how many diameters you draw, they all pass through the exact same point at the center.
In simple words: The center is where all the creases (diameters) meet in the middle. Every diameter goes through the center.

Exam Tip: The center of a circle is always where all diameters intersect - this is how you can find the center if you have drawn or marked several diameters.

Question 27. Measure the length of the creases from the center to the border of the circle. This is called the radius of the circle.
Answer: The measurement of the distance from the center to the border of the circle is called the radius. The radius is exactly half the length of the diameter. The actual measurement depends on the size of the circular paper being used - different circles will have different radii. What remains constant is the relationship: the radius is always half the diameter, regardless of the circle's size.
In simple words: The radius is the distance from the middle of the circle to the edge. It depends on how big your circle is.

Exam Tip: The radius is always half the diameter - so if you know the diameter, you can quickly find the radius by dividing by 2.

Question 28. Discuss if there is any relationship between the radius and the diameter of a circle.
Answer: Yes, there is a direct relationship between the radius and the diameter of a circle. The diameter is always exactly twice the radius. Equivalently, the radius is always half the diameter. This relationship holds true for all circles, regardless of their size. If you know the radius, multiply it by 2 to find the diameter. If you know the diameter, divide it by 2 to find the radius.
In simple words: The diameter is twice as long as the radius. The radius is half as long as the diameter. They are connected: diameter = 2 × radius.

Exam Tip: Remember the key formula: Diameter = 2 × Radius, or Radius = Diameter ÷ 2 - this relationship is essential for all circle problems.

Question 29. The length of the diameter is _____ (half/double) of the length of radius.
Answer: The length of the diameter is double the length of the radius. The diameter is twice as long as the radius in any circle.
In simple words: The diameter is two times bigger than the radius.

Exam Tip: Double (or twice) is the correct answer - the diameter is always twice the radius.

Question 30. Look at the carpet design. A beautiful circle, right? Mark the centre, radius, and the diameter of the circular design with any colour of your choice.
Answer: This is a practical activity where students identify and mark these important parts of a circle on the given carpet design. To complete this task: First, locate and mark the center of the circle - this is the middle point. Next, draw and mark a radius - a line from the center straight out to the edge of the circle. Finally, draw and mark a diameter - a line that goes all the way across the circle, passing through the center and touching the circle at two opposite points. Students may use any color they prefer to clearly show these three elements on the carpet design.
In simple words: Find the middle point (center), draw a line from the middle to the edge (radius), and draw a line all the way across through the middle (diameter).

Exam Tip: The diameter always passes through the center and is twice as long as the radius - mark these clearly so they are easy to see on the design.

Question 31. Look at the wheels. All wheels look like…
Answer: All wheels look like circles. Each wheel, whether from a car, bicycle, or any other vehicle or object, has a circular shape. The round form allows wheels to roll smoothly and move in all directions.
In simple words: All wheels are circles. Circles let wheels spin and roll easily.

Exam Tip: Recognizing that wheels are circular is important for understanding why circles are used in machinery and transportation.

Question 32. Name the wheel with the: (i) Longest radius (ii) Shortest radius (iii) Longest diameter (iv) Shortest diameter
Answer: (i) Wheel B has the longest radius. The radius is the distance from the center to the edge, and wheel B is visibly the largest of all the wheels shown.
(ii) Wheel D has the shortest radius. This wheel is the smallest, so it has the shortest distance from center to edge.
(iii) Wheel B has the longest diameter. Since the diameter is twice the radius, the wheel with the longest radius also has the longest diameter.
(iv) Wheel D has the shortest diameter. The smallest wheel will have the shortest diameter.
In simple words: Wheel B is the biggest, so it has the longest radius and diameter. Wheel D is the smallest, so it has the shortest radius and diameter.

Exam Tip: Comparing radii and diameters of circles is simple - the larger the wheel, the longer its radius and diameter.

Question 33. Identify the hidden shapes and write their names.
Answer: The hidden shapes in the image are: Square, Rectangle, Triangle, and Circle. Each of these basic shapes is embedded within the complex puzzle design. Students should carefully examine the overlapping lines and curves to identify these four fundamental geometric shapes.
In simple words: Look carefully at all the lines in the picture. You can find a square, a rectangle, a triangle, and a circle hiding in the design.

Exam Tip: When looking for hidden shapes, trace each shape's outline carefully - sometimes a shape is partially hidden behind other shapes.

Question 34. Draw 2 lines to divide the triangle into 1 square and 2 triangles.
Answer: To divide a triangle into 1 square and 2 triangles, follow these steps:
1. Draw one vertical line from a point on the top side of the triangle down to the opposite bottom side, creating a smaller triangle on the right and a quadrilateral on the left.
2. Draw a diagonal line from the top of the vertical line to the bottom right corner of the original triangle.
This creates one square on the left side and two triangles on the right side of the original triangle.
In simple words: Draw a straight line up and down on the left side to make a square. Draw another line from the top of that line to the bottom right corner. Now you have one square and two triangles.

Exam Tip: Start by identifying where the square should be - usually at one corner of the triangle - then draw lines that create that square while leaving two triangles in the remaining space.

Question 35. Draw 2 lines to divide the square into 3 triangles.
Answer: To divide a square into 3 triangles, follow these steps:
1. Draw one diagonal line from the top-left corner to the bottom-right corner of the square. This divides the square into 2 triangles.
2. Draw another line from the bottom-left corner to the midpoint of the top side of the square. This line divides one of the existing triangles into two smaller triangles.
The result is 3 triangles - one large triangle on the right and two smaller triangles on the left.
In simple words: Draw a diagonal line from the top-left to the bottom-right. Then draw another line from the bottom-left corner to the middle of the top side. Now you have three triangles.

Exam Tip: When dividing shapes with lines, start with one line that creates a basic division, then add a second line that splits one of the resulting pieces further.

Question 36. Draw lines to show the cuts needed on the shapes in the left column to get the smaller shapes on the right.
Answer: To transform the shapes on the left into the smaller shapes shown on the right, draw cut lines as follows:
For the shape requiring division into a rectangle and a triangle: Draw one horizontal line across the middle section to separate the upper rectangle from the lower triangle portion. Additionally, draw a vertical line on one side to further refine the shapes if needed.
For the shape that needs to become a triangle: Draw diagonal lines from the corners to isolate the triangular portion in the center or identify the triangle hidden within the larger shape.
The exact placement of lines depends on the specific shapes shown - carefully examine the target shapes on the right to determine where cuts should be made.
In simple words: Look at the small shapes on the right. Figure out what cuts (lines) you need to make on the big shapes on the left to create those smaller pieces.

Exam Tip: Match the outlines of the target shapes with the larger shape - the cut lines should separate the larger shape exactly along those outlines.

Page 21

Let Us Try

Question 1. Squiggly, the spider, likes to make webs in different shapes. One day she begins to make triangular webs. How many triangles are in her web?
Answer: There are 6 triangles in her web.
In simple words: Count all the small triangles and larger triangles formed by the lines together.

Exam Tip: When counting triangles, remember to count both the small individual triangles and the bigger ones made up of smaller triangles combined.

Question 2. She likes to take a walk each morning and check if the walls of her web are strong. Can she begin at point A and reach back to the same point without walking on any wall more than once?
Answer: Yes, she can! If she follows the web by walking along the numbered edges 1, 2, 3, 4, 5, ..., 11, 12 in order, she will return to point A without repeating any wall.
In simple words: By following a path that covers each wall only one time, she can come back to where she started.

Exam Tip: This type of problem tests whether a figure can be drawn without lifting the pen or crossing the same line twice - look for the Eulerian path in the network.

Question 3. Her brother, Wiggly made a web using rectangles. How many rectangles can you see in his web?
Answer: There are 6 rectangles in the web.
In simple words: Look for all rectangles - both the small single ones and larger ones formed by joining smaller rectangles together.

Exam Tip: Always count systematically - first the smallest unit rectangles, then combinations of 2, then combinations of 3, and so on.

Question 4. Can he begin at point A and leave from point B without walking on any wall more than once?
Answer: Yes, he can! One possible path is: A - right - down - left - down - right - B. Using this route ensures that no wall is walked on more than once.
In simple words: By choosing the right path through the web, you can go from A to B without using the same wall twice.

Exam Tip: When solving path problems, trace your route carefully and check off each edge as you use it to ensure no repetition.

Question 5. Use 5 matchsticks to make 2 triangles. Then draw it in the space provided.
Answer: Here's how you can do it: Start by making one large triangle using 3 matchsticks. Then use the remaining 2 matchsticks to make a smaller triangle either inside or beside the large one, with the two triangles sharing one common side. This arrangement creates 2 complete triangles using only 5 matchsticks total.
In simple words: Build one big triangle first, then add 2 more sticks to form a small triangle that shares a side with the big one.

Exam Tip: The key idea is sharing a side between shapes - this lets you use fewer matchsticks than if the shapes were separate.

Question 6. Move two matchsticks to make 4 triangles.
Answer: Move matchsticks to form a smaller triangle inside one of the larger triangles. This creates a total of 4 triangles: the 3 small triangles formed around the inner triangle, plus 1 large triangle making up the whole structure.
In simple words: Put a small triangle in the middle of a big triangle. Now you have 3 triangles around the edges plus 1 big triangle total.

Exam Tip: When rearranging matchsticks, think about how nested or overlapping shapes create multiple triangles to count.

Question 7. Remove 4 matchsticks to leave only 3 triangles.
Answer: Take away the matchsticks that form the top triangle and remove one side from a triangle in the bottom row. When you do this, 3 connected triangles will stay in place.
In simple words: Delete the top triangle and one edge of a bottom triangle, leaving exactly 3 triangles that are still joined together.

Exam Tip: Plan which sticks to remove so the remaining shapes stay connected - don't leave loose, separate triangles.

Question 8. Model Challenge - Can you make a model of solid shapes which has:
(a) 12 straws and 8 clay balls?
Answer: Yes, you can make a cube. A cube has 12 edges (straws) and 8 vertices or corners (clay balls).
In simple words: A cube needs 12 sticks for its edges and 8 balls for its corners.

Exam Tip: Remember that a cube has 8 corner points and 12 edges - this is a key property to memorize.

Question 9. Can you make a model of solid shapes which has 9 straws and 6 clay balls?
Answer: Yes, you can make either a triangular prism or a triangular pyramid. A triangular prism has 6 vertices (clay balls) and 9 edges (straws).
In simple words: A triangular prism or pyramid can be built with 6 corner points and 9 sticks for edges.

Exam Tip: A triangular prism has two triangular faces (one at each end) with 3 connecting edges between them.

Question 10. Can you make a model of solid shapes which has 15 straws and 10 clay balls?
Answer: Yes, you can make a pentagonal prism or similar five-sided solid shape. This 3D shape has 10 vertices (clay balls) and 15 edges (straws).
In simple words: A pentagonal prism (a shape with two 5-sided bases) has 10 corners and 15 edges.

Exam Tip: For prisms, the number of edges follows the pattern: 3 times the number of sides of the base shape (5 × 3 = 15 for a pentagon).

Question 11. Can you make a model of solid shapes which has 10 straws and 6 clay balls?
Answer: Yes, you can build a square pyramid. A square pyramid consists of 6 vertices (clay balls) - 4 at the base and 1 at the top, plus 1 at the center - and 10 edges (straws).
In simple words: A square pyramid has 6 corner points and 10 sticks connecting them as edges.

Exam Tip: A square pyramid has 4 edges around the square base, 4 slanting edges going up to the point, and 2 diagonals inside making 10 total.

Question 12. Classify these shapes based on the number of angles.
Answer:
Shapes with 3 angles: b, d, f
Shapes with 4 angles: a, c, g
Shapes with 5 angles: e
In simple words: Group shapes by counting how many corners or angles each one has - triangles have 3, quadrilaterals have 4, and pentagons have 5.

Exam Tip: The number of angles always equals the number of sides in any polygon - this is a universal rule.

Question 13. What relation do you notice between the number of sides and the number of angles?
Answer: The number of angles in a shape is exactly equal to the number of sides it has. Every corner of a polygon is where two sides meet, and that meeting point forms an angle.
In simple words: If a shape has 5 sides, it will have 5 angles. The number of angles always matches the number of sides.

Exam Tip: This relationship holds true for all polygons - remember that each side contributes to creating one angle.

Question 14. Draw a 2D shape that has less than 5 angles. Draw a 2D shape with more than 5 angles.
Answer: For a shape with less than 5 angles, you can draw a triangle (3 angles) or a quadrilateral (4 angles). For a shape with more than 5 angles, you can draw a hexagon (6 angles), a heptagon (7 angles), or an octagon (8 angles). Your own drawings of these shapes would be the answer.
In simple words: Triangles and squares have fewer than 5 angles. Hexagons and octagons have more than 5 angles.

Exam Tip: When drawing, make sure all sides are closed and clearly marked, with all angles shown at the corners.

Question 15. Mark the right angles and write the number of right angles in each figure.
Answer:
1st shape (blue rectangle): 4 right angles
2nd shape (green parallelogram): 0 right angles
3rd shape (purple triangle): 1 right angle
4th shape (yellow quadrilateral): 1 right angle
5th shape (violet irregular shape): 1 right angle
6th shape (red square): 4 right angles
In simple words: Mark each corner that forms a square corner (90 degrees) and count how many you find in each shape.

Exam Tip: Right angles look like perfect square corners - mark them with a small square symbol in the corner for clarity.

Question 16. Which shapes have only right angles?
Answer: The rectangle (1st shape) and the square (6th shape) are the only shapes that have only right angles. Every angle in these two shapes is exactly 90 degrees.
In simple words: Only rectangles and squares have all four corners as right angles - no other shape does.

Exam Tip: Remember that all right angles measure exactly 90 degrees, and these are the defining features of rectangles and squares.

Question 17. Observe the shapes and answer - Match each description to the correct shape:
(1) 2 right, 1 acute, 1 obtuse
(2) 1 right, 2 obtuse, 1 acute
(3) 2 obtuse, 2 acute
(4) 4 right angles
Answer:
(1) 2 right, 1 acute, 1 obtuse - Shape 14
(2) 1 right, 2 obtuse, 1 acute - Shape 2
(3) 2 obtuse, 2 acute - Shape 13
(4) 4 right angles - Shape 6
In simple words: Study each shape, identify whether its angles are acute (less than 90°), right (exactly 90°), or obtuse (more than 90°), then match it to the description that fits.

Exam Tip: Always examine all four angles of each quadrilateral carefully - note whether each angle is sharp (acute), square (right), or wide (obtuse) before matching.