NCERT Solutions for Class 3 Maths Chapter 05 Fun with Shapes

Chapter 5: Fun with Shapes

Question 1. Make Amma's rangoli on the dots given below.
Answer: This is a fun drawing activity! You can connect the dots with straight lines and curves to copy the colorful rangoli pattern shown in the picture.
In simple words: Connect the dots using straight and curved lines to draw a colorful geometric rangoli pattern.

Exam Tip: Use a sharp pencil to draw the straight lines between the dots so your rangoli looks neat and symmetrical.

Question 2. Name the shapes drawn in Amma's rangoli: ________, ________, ________
Answer: The three shapes used in Amma's rangoli are: Square, Triangle, and Circle.
In simple words: Amma used squares, triangles, and circles to build her beautiful design.

Exam Tip: Practice identifying basic shapes (squares, circles, and triangles) in traditional Indian art and decorations.

Question 3. How many shapes are made with
(i) Curved lines ________
(ii) Straight lines ________
Answer: Based on the shapes in the rangoli:
* (i) Shapes with curved lines: 1 (which is the Circle)
* (ii) Shapes with straight lines: 2 (which are the Square and the Triangle)
In simple words: The circle is made of a curved line. The square and triangle are made of straight lines.

Exam Tip: Remember that circles are made with curved lines, while polygons like triangles and squares are made with straight lines.

Question 4. Use shapes and objects from the classroom to make a rangoli design. Outline the object and colour.
Answer: This is a creative tracing activity. You can place things like your circular water bottle cap, rectangular pencil box, and flat scale on paper, trace their outlines with a pencil, and color them in to make a beautiful design.
In simple words: Trace around real classroom items like notebooks, bottles, and scales to create your own geometric art.

Exam Tip: Hold the objects firmly with one hand while tracing so your lines do not wiggle or get distorted.

Question 5. Try to make the following objects using shape cutouts.
Answer: We can cut out bright shapes from colored paper (like triangles, circles, and squares) and glue them together on a page to build pictures of a sailing boat, a flitting butterfly, and a flying rocket.
In simple words: Paste paper triangles and circles together to build cute pictures of rockets, boats, and butterflies.

Exam Tip: Cut out a variety of different sized triangles first, as they are used for the sails, wings, and rocket tips.

Question 6. Let us Do. Question 1 : Collect some cardboard boxes and open them up carefully. What shapes do you see in the flattened boxes?
Answer: When we open and flatten cardboard boxes, we can see flat shapes like squares, rectangles, and other flat shapes with many straight sides (polygons).
In simple words: Opening a cardboard box shows that it is made from flat paper rectangles and squares folded together.

Exam Tip: Opening a 3D box flat is a great way to understand what a "net" of a 3D shape is in mathematics.

Question 7. Question 2 : Make an Envelope. Use a square piece of paper and fold it as shown in the picture.
Answer: This is a fun paper-folding (origami) activity. You can fold the four corners of a square paper toward the center to make a neat little envelope.
In simple words: Take a square sheet of paper and fold its corners to meet in the middle to make a paper envelope.

Exam Tip: Crease each fold tightly with your thumbnail so that your paper envelope stays closed and neat.

Question 8. Question : Why did the two children get different shapes? Discuss.
Answer: The children got different shapes because the boxes they traced were different. The wooden box has square faces, while the matchbox has rectangular faces.
In simple words: The children got different outlines because they traced different boxes. One box was a cube, and the other was a cuboid.

Exam Tip: Tracing the flat faces of 3D solids always produces 2D shapes like squares or rectangles.

Question 9. Question : Name any three objects that have rectangular faces.
Answer: Three common objects with flat, rectangular sides are: a lunch box, a matchbox, and a pencil box.
In simple words: Notebooks, bricks, and pencil boxes are examples of items that have flat rectangular faces.

Exam Tip: Think of standard cuboid items in your schoolbag to quickly name objects with rectangular faces.

Question 10. Let us Do. Question 1 : Trace all the faces of any cuboidal object. (example - sharpener or eraser)
(a) How many different faces did you get? ________
(b) What shapes are these faces? ________
(c) Did you get a square? ________
(d) Can you get six different rectangles by tracing a cuboid? ________
(e) Can a cuboid have a face like a triangle? ________
(f) The faces of a cuboid are ________ or ________ in shape.
Answer: Based on tracing our classroom eraser and sharpener:
* (a) We get 2 different types of faces (squares and rectangles).
* (b) These flat faces are in the shape of squares and rectangles.
* (c) Yes, we can get a square face.
* (d) No, we cannot get six completely different rectangles (some opposite faces will be identical).
* (e) No, a cuboid cannot have a triangular face.
* (f) The faces of any cuboid are always in the shape of a square or a rectangle.
In simple words: Tracing a cuboid's six sides will only give you flat squares and rectangles. It can never have triangular sides.

Exam Tip: A standard cuboid always has exactly 6 faces, but some of these faces are identical to each other.

Question 11. Question 2 : Construct the rectangles using the sides given below. (Dot grid activity)
Answer: You can use a ruler to connect the dots and complete the rectangular shapes on the grid.
In simple words: Connect the dots on the grid to close the open lines and make complete rectangles.

Exam Tip: Rectangles must have four straight sides where opposite sides are equal and all corners are straight L-shapes.

Question 12. Question 3 : Draw 3 bigger rectangles around this small rectangle.
Answer: Draw three larger rectangular borders around the small center rectangle, with each new box being bigger than the last one.
In simple words: Draw three bigger rectangular boxes around the small one, like borders on a photo frame.

Exam Tip: Make sure the sides of your new larger rectangles do not touch each other or cross lines.

Question 13. Question 4 : Count and write the number of rectangles in the following picture. ________
Answer: There are exactly 8 rectangles in the given picture.
In simple words: When we count the single small boxes and the larger joined boxes, we find eight rectangles in total.

Exam Tip: Don't just count the single small boxes; look for larger rectangles made by joining two or three small boxes together.

Question 14. Question 5 : Look at the different rectangles given below and answer the following questions.
(a) How many sides are there in a rectangle? ________
(b) How many corners are there in a rectangle? ________
(c) Are there any sides in a rectangle that are equal in length to each other? ________
(d) What do you notice in a rectangle? Describe it in your own words.
Answer: Based on the properties of rectangles:
* (a) A rectangle has 4 sides.
* (b) A rectangle has 4 corners (vertices).
* (c) Yes, there are sides of equal length.
* (d) What we notice: The opposite sides (the sides facing each other) in a rectangle are always equal in length.
In simple words: A rectangle has four sides and four corners. Its opposite sides are always of the same length.

Exam Tip: Remember that "opposite sides are equal" is the most important rule that defines a rectangle.

Question 15. Question :
1. Both have ________ sides.
2. Both have ________ corners.
How many squares do you see in this drawing? [ ]
Answer: Based on squares and rectangles:
* 1. Both a square and a rectangle have 4 sides.
* 2. Both have 4 corners.
* The total number of squares we can see in this drawing is 6 (which are highlighted in red in the solved steps).
In simple words: Squares and rectangles both have 4 sides and 4 corners. In this complex box drawing, we can find six squares.

Exam Tip: When counting squares in a grid, look for both small single squares and larger squares made of four smaller ones.

Question 16. Let us Do. Question : Here is a square. Draw 2 bigger squares around this square.
Answer: Draw two larger square boxes around the center square, making sure all four sides of each new box are equal.
In simple words: Draw two larger squares enclosing the small one, keeping all sides equal.

Exam Tip: A square must have all four sides of equal length. Use the dot grid spacing to make sure you count the same number of dots for all four sides.

Question 17. Question : Use matchsticks to make a square so that it has squares on all its sides. How many squares did you get?
Answer: By arranging matchsticks in a cross shape, we can build 5 squares in total (four outer squares on each side and one square in the middle).
In simple words: Stacking matchsticks in a cross layout gives us five separate squares.

Exam Tip: Use 12 matchsticks to build this cross shape. Count the middle square as the fifth one.

Question 18. Question : Complete the squares using the sides given below.
Answer: Connect the dots on the grid to complete the square shapes.
In simple words: Join the unfinished lines on the dot sheet to make complete, equal-sided squares.

Exam Tip: Check that the vertical and horizontal side lengths have the same number of dot spaces so it stays a square.

Question 19. Question : Use the square cutouts from the book to do this activity. How many different shapes can you make by joining
(a) 2 squares
(b) 3 squares
(c) 4 squares
Show them in a dot grid. Some dot grids are provided in the back of the book.
Answer: Using square paper cutouts, we can join them edge-to-edge to make different flat patterns:
* (a) With 2 squares: We can make only 1 shape (a domino rectangle).
* (b) With 3 squares: We can make 2 different shapes (a straight line of 3 and an L-shape).
* (c) With 4 squares: We can make 5 different shapes (called tetrominoes, including a square, a straight line, an L-shape, a T-shape, and a zig-zag shape).
In simple words: Joining square tiles together in different ways lets us build flat shapes, just like playing Tetris!

Exam Tip: Make sure the squares are joined along complete edges, not just touching at the corners.

Question 20. Question 1 : Tick (✓) the shapes that are rectangles.
Answer: Look for shapes with 4 straight sides where opposite sides are equal and all corners are perfect L-shapes. We put a checkmark (✓) on those rectangles.
In simple words: We put a checkmark on any four-sided shape that has straight lines and perfect right-angle corners.

Exam Tip: Slanted shapes (like parallelograms) are not rectangles because their corners are not perfect L-shapes.

Question 21. Question 1 : Which figures are not rectangles? Explain why.
Answer: The shapes marked with an 'X' are not rectangles. This is because their sides are slanted, and their corners are not perfect L-shapes.
In simple words: Shapes with slanted lines and sharp or wide corners are not rectangles because their corners are not L-shaped.

Exam Tip: A shape must have four straight sides and four right angles (90 degrees) to be called a rectangle.

Question 22. Question 2 : Can you fold all the corners of a square sheet in such a way that the number of corners remains the same?
Answer: Yes, if we fold all four corners of a square paper flat inward toward the center, the new folded shape will still have exactly 4 corners.
In simple words: Yes, folding the four points of a square inward makes a smaller shape that still has four corners.

Exam Tip: Try this folding activity with a real square sheet of paper to see how the four old corners become four new corners.

Question 23. Question 3 : Make a square on a cardboard sheet and cut along the dotted lines marked on the square as shown to get 4 triangles. Make as many different shapes as possible by joining three triangles together. How many shapes can you make? Now try with four triangles together.
Answer: By cutting a square along its diagonals, we get 4 equal triangles. By joining these triangles edge-to-edge, we can build different geometric shapes like a large triangle, a diamond shape, or a parallelogram.
In simple words: Cutting a square gives us four triangles. Joining them back in different ways lets us make diamonds, triangles, and oblong shapes.

Exam Tip: This is a puzzle. Try joining the longest sides of the triangles together first to see what shapes you get.

Question 24. Question : Are the corners of a square the same?
Answer: Yes, all four corners of a square are exactly the same.
In simple words: Yes, every corner of a square looks identical.

Exam Tip: Since all four sides of a square are equal, all its four corners are also equal.

Question 25. Question : How do you know?
Answer: We can tell because every corner forms a perfect, straight L-shape (which is a right angle).
In simple words: We know because each corner is a straight L-shape.

Exam Tip: In math, a perfect L-shaped corner is called a right angle or a square corner.

Question 26. Question : Are the corners of a rectangle the same?
Answer: Yes, all four corners of a rectangle are also exactly the same.
In simple words: Yes, all corners of a rectangle are identical.

Exam Tip: Both squares and rectangles share the same corner property - they all have right angles.

Question 27. Question : How do you know?
Answer: Just like a square, all the corners of a rectangle make a perfect, straight L-shape.
In simple words: We know because each corner is a perfect L-shape, just like in a square.

Exam Tip: You can test any corner with a folded paper strip to see if it makes a perfect L-shape.

Question 28. Question : Are the corners of the square and a rectangle the same?
Answer: Yes, the corners of a square and a rectangle are identical because they are both straight L-shaped corners.
In simple words: Yes, both squares and rectangles have the same kind of flat L-shaped corners.

Exam Tip: This shared property is why squares and rectangles are closely related shapes in geometry.

Question 29. Question : Name some objects in your class that have only square corners.
Answer: Some classroom objects with only straight, square corners are: the green board, erasers, lunch boxes, books, notebooks, desks, windows, and the ceiling.
In simple words: Everyday school items like books, green boards, and desks have only straight, square corners.

Exam Tip: Look at the edges of your notebook to find an easy example of a square corner.

Question 30. Question : Can you use the strip to check whether the corner of your table and the board are square corners?
Answer: Yes, we can place our paper folding strip against the corners of our study table and the school board. This test proves that both have perfect square corners.
In simple words: Yes, using a paper strip helps us prove that the table and board have perfect square corners.

Exam Tip: A paper corner tester is a great, simple tool you can make in 10 seconds to check angles.

Question 31. Question 1 : Mark the square corners in these shapes.
Answer: We can look at each shape and draw a small circle around any corner that makes a perfect, straight L-shape. This happens on all corners of the square and the rectangle.
In simple words: We put a small circle around the straight L-corners of the square and the rectangle.

Exam Tip: Tilted shapes like diamonds or pentagons do not have standard square corners.

Question 32. Question 2 : Connect the dots to make some squares. How many different squares did you get?
Answer: By connecting the dots, we can make 2 different squares (one straight square and one tilted square).
In simple words: Connecting the dots lets us draw two types of squares on the grid.

Exam Tip: Remember that a tilted square is still a square because all its four sides are equal and its corners are L-shaped.

Question 33. Question 3 : Look at the picture given below and answer the following.
a. Count and write the number of corners. [ ]
b. Circle the square corners.
Answer: Based on the sailboat drawing:
* a. There are exactly 13 corners on the sailboat drawing.
* b. We draw a circle around any corner on the boat that forms a straight L-shape (like the corners of the sails and the deck).
In simple words: The boat has thirteen corners in total, and we circle the ones that make a straight L-shape.

Exam Tip: Count the corners of each sail separately, then count the corners of the wooden boat base to get the correct total.

Question 34. Question 4 : Use two matchsticks to make two square corners and then four square corners. Draw and show it in the space given below.
Answer: Here is how we place the matchsticks:
* To make two square corners, we can place two matchsticks to form a T-shape.
* To make four square corners, we can cross two matchsticks in the middle to form a plus (+) shape.
In simple words: A T-shape has two square corners, and a cross shape (+) has four square corners.

Exam Tip: Draw the matchsticks with their small round heads so that your diagram looks realistic and clear.

Question 35. Question 5 : Murugan made three squares with 10 matchsticks. How many squares can you make with 12 matchsticks?
Answer: We can make 5 squares in total using 12 matchsticks by arranging them in a 2x2 grid (four small squares inside and one large outer square).
In simple words: Twelve matchsticks can build four small squares that join to make one large square, giving us five squares.

Exam Tip: Don't forget to count the large outer square as the fifth square of your model.

Question 36. Describe a Triangle. Triangles have ________ sides. They have ________ corners.
Answer: A triangle has 3 sides and 3 corners.
In simple words: Any triangle shape is made of three straight lines and has three pointed corners.

Exam Tip: "Tri" means three, which is why a triangle always has three sides and three corners.

Question 37. Let us Do. Question 1 : Draw and name some triangular objects, that you see around you, in your notebook.
Answer: Some triangular objects we see in daily life are: a tall mountain peak, a slice of cheese, a slice of pizza, and an ancient Egyptian pyramid.
In simple words: Slices of pizza, cheese, and high mountain peaks are shaped like triangles.

Exam Tip: Name simple everyday items that have exactly three straight sides to answer this question.

Question 38. Question 2 : Count the number of triangles in the given rangoli.
Answer: Based on counting the design shapes:
* Rangoli pattern (a) has exactly 16 triangles.
* Rangoli pattern (b) has exactly 16 triangles.
In simple words: Both colorful rangoli patterns are made from sixteen small triangles joined together.

Exam Tip: Count the small outer triangles first, then look inside the center star to count the rest.

Question 39. Question 3 : How many different triangles can be made using the dots on this circle?
Answer: We can draw exactly 4 different triangles by connecting the dots on this circle.
In simple words: By joining the dots on the circle with straight lines, we can make four triangles.

Exam Tip: Connect any three dots on the circle with straight lines to form a triangle.

Question 40. Question 4 : Move two matchsticks to turn the one triangle into two triangles.
Answer: Take two matchsticks from the outer sides and place them down the middle of the large triangle. This splits it into two smaller triangles.
In simple words: Moving two sticks to make a center line splits the large triangle into two small ones.

Exam Tip: Drawing a line inside a triangle from one corner to the opposite side always splits it into two triangles.

Question 41. Let us Discuss. Question 1 : Have you been to a circus?
Answer: No, I have not visited a real circus yet, but I enjoy watching acrobats and clowns performing tricks on television and in picture books.
In simple words: I have not been to a circus, but I love seeing circus clowns and animals in books.

Exam Tip: You can share what you have seen in books or movies if you have not visited a circus in person.

Question 2. What does a circle look like? How is a circle different from a rectangle?
Answer: A circle is completely round. It has no straight lines and no sharp corners. A rectangle is different because it has 4 straight sides and 4 sharp corners.
In simple words: A circle is round and has no corners. A rectangle is boxy with four straight sides and four corners.

Exam Tip: Highlight that circles have curved lines, while rectangles are made using only straight lines.

Question 1. Let us Do. Name some objects that are like circles.
Answer: Some round, circular objects we use daily are: bicycle wheels, car tires, metal coins, eating plates, wall clocks, and shirt buttons.
In simple words: Round things like coins, plates, clocks, and wheel tires are shaped like circles.

Exam Tip: Look at your uniform buttons or pocket coins to quickly name circular objects.

Question 2. Draw colourful circles to complete the circus scene.
Answer: Use your colored pencils to trace over the dotted circles. This will complete the juggler's ring, the dog's hoop, and the clown's unicycle wheel.
In simple words: Tracing the dotted lines with colored pens completes the round rings in the circus scene.

Exam Tip: Try tracing slowly so your circle lines stay smooth and do not get wobbly.

Question 3. Draw circles by tracing bottle caps, bangles, and rings in your notebook.
Answer: This is a fun tracing activity. Place a round bottle cap, a plastic bangle, or a finger ring on your page, trace around its edge with a pencil, and you will get perfect circles!
In simple words: Tracing around circular items like bangles or bottle lids is an easy way to draw perfect circles.

Exam Tip: Press the cap down firmly so it does not slide while you draw around it.

Question. Have you played any game where you need to draw a circle? Try to make a circle on the playground.
Answer: Yes, we play games like Kho-Kho where we must draw circular rings on the playground for players to sit. We also draw circles when playing outdoor games like ring-toss.
In simple words: Yes, we draw round circles on the play field when playing Kho-Kho or running games.

Exam Tip: You can use a piece of chalk tied to a string to draw a perfect, large circle on the playground.

Question 1. Let us Do. Look at these two shapes and discuss their similarities and differences. Tick (✓) the appropriate word.
a. Their corner are [same] [different]
b. Number of sides is [same] [different]
Answer: Based on comparing the red square and green triangle:
* a. Their corners are: different (✓) (The square has 4 square corners, but the triangle has 3 pointed corners).
* b. The number of sides is: different (✓) (The square has 4 sides, but the triangle has 3 sides).
In simple words: A square and a triangle have different numbers of sides and different kinds of corners.

Exam Tip: A square always has four straight L-corners, while a triangle has three sharp corners.

Question 3. Choose any pair of shapes. Share the similarities and differences in these shapes with your friends.
Answer: When comparing geometric shapes:
* How they are the same: All of these shapes are built using only straight lines.
* How they are different: They all have a different number of sides and corners. For example, a triangle has 3 sides, but a hexagon has 6 sides.
In simple words: These shapes are all made of straight lines, but they have different numbers of sides.

Exam Tip: Count the straight sides of any shape to find out if it is a triangle, square, or pentagon.

Question 4. Find the largest rectangle in these shapes.
Answer: By drawing a thick border, we can find the biggest possible rectangle hiding inside each of these irregular grid shapes.
In simple words: We can outline the largest boxy rectangle that fits inside each of the yellow shapes on the grid.

Exam Tip: Look for the longest rows and columns of full square boxes to find the largest rectangle.

Question 5. I made one triangle. Then I made another row of triangles. How many triangles are there in the second figure? If I make one more row, how many triangles will there be in the third figure?
Answer: Based on the triangle rows:
* In the second figure, we can find 4 small triangles and 1 large outer triangle, making 5 triangles in total.
* In the third figure, we can count 9 small triangles, 3 medium-sized triangles, and 1 large outer triangle, making 13 triangles in all.
In simple words: The second figure has five triangles in total, and the third figure has thirteen triangles.

Exam Tip: When counting, look for nested triangles made of smaller triangles grouped together.

Question 6. Here are some rectangles that are torn. How many square pieces have been torn from each shape?
Answer: Let us count the missing square blocks for each torn shape:
* First shape has 3 missing squares.
* Second shape has 8 missing squares.
* Third shape has 9 missing squares.
* Fourth shape has 7 missing squares.
* Fifth shape has 2 missing squares.
* Sixth shape has 4 missing squares.
In simple words: We can count the empty white squares to find how many grid pieces are missing from each torn shape.

Exam Tip: Use a pencil to complete the grid lines over the torn area to make counting the missing squares very easy.

Question 7. Each of these shapes can be the odd one out. How is each one odd? Discuss.
Answer: Each shape can be the odd one out for its own special reason:
* The Red Square: It is the only shape with a round white hole cut out in the center.
* The Orange Square: It is the smallest shape on the page.
* The Blue Triangle: It is the only shape with 3 sides (the others all have 4 sides).
* The Green Square: It is the only plain, solid shape without any holes, size changes, or different angles.
In simple words: Every shape is unique. The triangle is the only three-sided shape, and the red square has a round hole.

Exam Tip: "Odd one out" depends on properties like size, color, number of sides, or empty spaces.

Question 8. To complete the rectangle, tick (✓) the appropriate shapes from the left side to fill the gaps in the shape on the right side.
Answer: We can put a checkmark (✓) on the exact puzzle pieces on the left that will fit perfectly into the empty white gaps on the right to complete the rectangular grid.
In simple words: Choose the matching grid shapes that fit like puzzle pieces into the white spaces on the right.

Exam Tip: Count the number of squares in each white gap to find the matching shape from the choices.

Question 9. Draw two lines to split the shape into three triangles.
Answer: Draw one straight line down from the top point to the bottom floor, and draw another diagonal line across one of the boxes. This splits the house shape into three neat triangles.
In simple words: Drawing two straight lines through the house shape divides it into three triangles.

Exam Tip: Triangles must have exactly three straight sides. Make sure your lines connect the corners of the shape.

Question 10. Draw one line to split the shape into 3 triangles.
Answer: Draw one diagonal line connecting the inner corner to the opposite outer corner of the L-shape. This will split the shape into three triangles.
In simple words: Drawing a single diagonal line across the inner corner of the L-shape splits it into three triangles.

Exam Tip: Practice drawing different diagonal lines on L-shapes to see how they form triangles.

Question 11. Make the following shapes with different sizes and orientations (angular positions) in your notebook.
(a) Triangle
(b) Rectangle
(c) Circle
(d) Other shape
Answer: Draw a variety of basic shapes in different sizes (some small, some large) and turn them in different directions (like a tilted rectangle or a sideways triangle) to practice your drawing skills.
In simple words: Draw circles, rectangles, and triangles in different sizes and turn them in different directions on your page.

Exam Tip: Turning a shape (rotating it) does not change its name. A tilted triangle is still a triangle!