NCERT Solutions Class 5 Mathematics Mela Chapter 07 Shapes and Patterns

Page 93

Let Us Try

Question. Draw the following pattern on a grid paper. Part of it is done for you. Now, complete the rest of the grid to get the full design.
Answer: [Student activity - complete the grid pattern by continuing the yellow squares on a green background to form the full design as shown in the answer image]
In simple words: Look at the part that is already done. Keep adding yellow squares in the same way to fill up the rest of the grid and make the complete picture.

Exam Tip: Pay careful attention to the colours and the pattern of how the squares are placed - follow the exact same pattern across the whole grid.

Page 94

Find Out

Question. Can regular triangles fit together at a point without any gap? How many of them fit together?
Answer: Yes, regular triangles can join together. A total of 6 triangles can meet at a single point. The corners of all 6 triangles will touch perfectly with no spaces between them.
In simple words: Six triangles fit around one point with no gaps.

Exam Tip: Remember that the angle at each corner of a regular triangle is 60 degrees, and 360 ÷ 60 = 6, so exactly six fit around a point.

Question. Can squares (a regular 4-sided shape) fit together around a point without any gap or overlap?
Answer: Yes, squares can join around a point with no space between them and no overlap. The total angle around a point is 360 degrees, and each corner angle of a square is 90 degrees. When we divide: 360 degrees ÷ 90 degrees = 4. So exactly four squares fit around a point perfectly.
In simple words: Four squares fit around a point because 4 times 90 degrees equals 360 degrees.

Exam Tip: The key is understanding that all angles around a point must add up to exactly 360 degrees - no more, no less.

Question. Can five squares fit together around a point without any gaps or overlaps? Why or why not?
Answer: No, five squares cannot fit together around a point. Each square has a corner angle of 90 degrees. If we try to place five squares, we would need 5 times 90 = 450 degrees of space total. However, a full circle around a point is only 360 degrees. Since 450 is more than 360, the squares will either overlap or leave gaps.
In simple words: Five squares need too much space - they would need 450 degrees but only 360 degrees is available around a point.

Exam Tip: Always check whether the corner angles multiply to equal 360 degrees - if they add up to more, shapes won't fit; if less, gaps will appear.

Question. Can regular hexagons (6-sided shapes with equal sides) fit together around a point without any gaps or overlaps?
Answer: Yes, regular hexagons can fit together around a point without any space or overlap. The angle at each corner of a regular hexagon is 120 degrees. The total angle around a point is 360 degrees. When we divide: 360 degrees ÷ 120 degrees = 3. So exactly three hexagons fit together perfectly around a point.
In simple words: Three hexagons fit around a point because 3 times 120 degrees equals 360 degrees.

Exam Tip: Use the formula: number of shapes = 360 ÷ corner angle. This works for any regular shape.

Page 95

Question. Here is a tessellating pattern with more than one shape. What shapes have been used in this pattern?
Answer: This pattern is made up of equilateral triangles and regular hexagons.
In simple words: The pattern uses two types of shapes - triangles and hexagons.

Exam Tip: When identifying shapes in a pattern, count the sides carefully - triangles have 3 sides, hexagons have 6 sides.

Question. Continue the pattern given below and colour it appropriately.
Answer: [Student activity - continue the tessellating pattern by alternating yellow triangles and purple hexagons in the same arrangement shown in the answer image]
In simple words: Keep placing triangles and hexagons in the same order, using the same colours, to extend the pattern further.

Exam Tip: Look at how the shapes link together - follow that same connection pattern when you add more shapes.

Question. Do regular octagons fit together without any gaps or overlaps? Try drawing the same and check.
Answer: No, regular octagons do not fit together without spaces or overlaps. When we try to place octagons side by side, we will always see gaps between them or overlapping edges. This is because the corner angle of a regular octagon (135 degrees) does not divide evenly into 360 degrees.
In simple words: Octagons leave gaps or overlap because their corner angles don't match up perfectly around a point.

Exam Tip: Test the rule: 360 ÷ 135 = 2.67, which is not a whole number, so octagons cannot tessellate on their own.

Page 96

Question. Look at the pattern given below. What shapes are coming together at the marked points? Are the same set of shapes coming together at these points?
Answer: At each marked point in this pattern, two octagons and one square come together. Yes, the same set of shapes - two octagons and one square - meet at all the red-marked points throughout the pattern.
In simple words: At every marked point, you see exactly two octagons and one square meeting.

Exam Tip: In a regular tessellation pattern, the same arrangement of shapes appears at every marked point - this shows the pattern repeats correctly.

Question. Continue the pattern and colour it appropriately.
Answer: [Student activity - extend the octagon-square pattern by continuing to place two octagons and one square at each marked point, maintaining the same colours as shown]
In simple words: Keep the same pattern of octagons and squares, with the same colours, as you fill in the rest of the space.

Exam Tip: Make sure each new point you mark has exactly the same arrangement - two octagons and one square - before you colour.

Question. Here is a tiling pattern made using two different shapes - squares and triangles. Are the triangles equilateral? Why or why not?
Answer: No, the triangles in this pattern are not equilateral. An equilateral triangle has all three sides the same length and all angles equal to 60 degrees. In this tiling pattern, the triangles placed with the squares are not equilateral because their sides are not all the same length. Two of the triangle's sides match the side of the square, but the third side is smaller than the other two.
In simple words: These triangles are not equilateral because not all their sides are the same length.

Exam Tip: Remember - equilateral means all three sides are equal. If even one side is different, it is not equilateral.

Question. What shapes are coming together at the marked points?
Answer: At the marked points, a square and two triangles touch each other. Three shapes meet in total - one square and two triangles.
In simple words: At each marked point, you see one square and two triangles meeting.

Exam Tip: Count carefully - identify each shape type and how many of each type appears at the point.

Question. Are the same set of shapes coming together at these points? Continue the pattern and colour it appropriately.
Answer: Yes, at each marked point in the pattern, the same group of shapes meets - one square plus two triangles. This tells us the pattern is regular and repeating, which is what tessellation needs to be.
In simple words: Yes, the same shapes (one square and two triangles) meet at every marked point in the pattern.

Exam Tip: A regular tessellation pattern repeats the same arrangement everywhere - check that every marked point has identical shape combinations.

Question. Create similar patterns using other cutouts of shapes.
Answer: [Student activity - create new tessellating patterns using other shape cutouts, arranging them so they fit together without gaps or overlaps]
In simple words: Make your own tessellation by fitting shapes together with no gaps or overlaps, similar to the patterns you just studied.

Exam Tip: Before finalizing your pattern, check that all marked points have the same arrangement of shapes repeated throughout.

Page 97

Question. What geometrical shapes can you make by fitting 2 of these triangles together? Trace the shapes you created.
Answer: By fitting two triangles together in different ways, you can create: a parallelogram, a triangle, a rectangle, and a kite.
In simple words: Two triangles can be arranged to make four different shapes.

Exam Tip: Try rotating and flipping the triangles in different ways - each new position creates a different shape.

Question 1. How many different types of triangles can you make? Now, observe and measure the sides of these triangles. What do you notice?
Answer: You can make two different types of triangles. After measuring the sides carefully, you will find that these are isosceles triangles - meaning two of their sides are the same length and one side is different.
In simple words: You can make 2 different triangles, and they are both isosceles (two sides the same length).

Exam Tip: Isosceles triangles always have exactly two sides of equal length - measure carefully to confirm this.

Question 2. Is it possible to make a triangle where all three sides are equal (equilateral triangle)?
Answer: No, you cannot make an equilateral triangle by joining these two parts together. The shapes of the two parts do not allow you to form a triangle where all three sides are the same length.
In simple words: These two pieces cannot be put together to make an equilateral triangle.

Exam Tip: For an equilateral triangle, all three sides must be exactly equal - if the pieces don't support this, it cannot be formed.

Question 3. Is it possible to make a triangle where all three sides are unequal?
Answer: A single piece is already in the form of a scalene triangle. However, when you join two pieces together, they do not form a triangle whose all sides are unequal in a way that creates a scalene triangle.
In simple words: One single piece is a scalene triangle, but two pieces joined together do not make a proper scalene triangle.

Exam Tip: A scalene triangle has all three sides of different lengths - check that no two sides are equal.

Try This

Question. Cut the equilateral triangle provided at the end of the book. Check if all the angles of an equilateral triangle are equal. Now, cut the equilateral triangle in half. How many sides of each new triangle are equal?
Answer: Yes, all the angles of an equilateral triangle are equal - each angle is 60 degrees. When you cut the equilateral triangle in half, you create two new triangles. In each new triangle, you will see that all the sides are unequal, making them scalene triangles.
In simple words: An equilateral triangle has three equal angles. When you cut it in half, each piece has all different side lengths.

Exam Tip: An equilateral triangle has three 60-degree angles. When cut in half along a line through the middle, it creates two scalene triangles with no equal sides.

Question. Triangles that have no equal sides are called scalene triangles. Check in scalene triangles whether any two or more angles are equal.
Answer: In the scalene triangles that you create by cutting an equilateral triangle in half, all the angles are different from each other. No two angles are the same.
In simple words: In a scalene triangle, all three angles are different from each other.

Exam Tip: If all three sides of a triangle are different, then all three angles will also be different - this is always true for scalene triangles.

Question 4. How many different 4-sided shapes (quadrilaterals) can you make?
Answer: You can make three different quadrilaterals using the given pieces.
In simple words: You can create 3 different 4-sided shapes.

Exam Tip: When combining pieces to make quadrilaterals, try different arrangements and orientations to discover all possible shapes.

Question 5. Measure the sides of each of these two quadrilaterals A and B. What do you notice? Are there any pairs of sides that are equal? Which pairs are equal - adjacent or opposite?
Answer: In both shapes A and B, the opposite sides are equal - the top and bottom sides match each other, and the left and right sides match each other. However, in the first figure (the kite), adjacent sides are equal to each other, not opposite sides.
In simple words: In shapes A and B, opposite sides are equal. In a kite, the sides next to each other are equal.

Exam Tip: Opposite sides connect opposite corners (top-bottom, left-right). Adjacent sides meet at the same corner. Different shapes have different patterns of equal sides.

Question 6. In the grid given below, draw two different kites and parallelograms each.
Answer: [Student activity - draw two kites and two parallelograms on the grid, ensuring each shape is distinct from the others]
In simple words: Draw two different kites (with adjacent sides equal) and two different parallelograms (with opposite sides equal and parallel).

Exam Tip: Remember - kites have two pairs of adjacent equal sides, while parallelograms have two pairs of opposite equal and parallel sides.

Question 7. Now, use 3 triangles from the rhombus to form shapes. How many sides do each one of them have?
Answer: [Student activity - arrange three triangle pieces from a rhombus to create new shapes and count the number of sides in each resulting shape]
In simple words: Use three pieces to make shapes and count how many sides each new shape has.

Exam Tip: Count the sides carefully by tracing around the outside edge of each shape you create.

Question 8. Which of these shapes can be made with all 4 pieces? Try and find out. (a) Square (b) Rectangle (c) Triangle (d) Pentagon (5-sided) (e) Hexagon (6-sided) (f) Octagon (8-sided)
Answer: (a) Square - possible (if you arrange the four pieces correctly).

If you divide a rhombus into four triangles using its diagonals, you get four identical right triangles. With these four pieces, only the square can be formed. The other shapes have the following results:

(b) Rectangle - possible. Two triangles can combine to form a rectangle, and combining two rectangles gives you a larger rectangle.

(c) Triangle - not possible. Four pieces cannot be arranged into a single perfect triangle.

(d) Pentagon (5-sided) - cannot be formed.

(e) Hexagon (6-sided) - possible, by arranging the four triangles with their longest sides facing outward.

(f) Octagon (8-sided) - not possible with just four pieces.

In simple words: You can make a square, a rectangle, or a hexagon. You cannot make a triangle, pentagon, or octagon with all 4 pieces.

Exam Tip: Try different arrangements of the four triangles to see which shapes can fit together - visualize how the angles and sides match up for each attempt.

Page 99

Tangram

Question. Look at the tangram set given at the end of your textbook. Cut out all the shapes. Name them.
Answer: The tangram set contains seven shapes: five triangles (of different sizes), one square, and one parallelogram.
In simple words: A tangram has seven pieces - triangles, a square, and a parallelogram.

Exam Tip: Learn the names of all seven tangram pieces - knowing their shapes will help you use them to make other figures.

Question (a). How are they same or different from each other?
Answer: Shapes 1, 2, 3, 5, and 6 are all triangles. Of these triangle shapes, shapes 2 and 3 are identical (equal in size), and shapes 1 and 5 are also identical to each other. Shape 4 is a square with all sides and angles equal. Shape 7 is a parallelogram with opposite sides and angles equal.
In simple words: Some tangram pieces are the same size and shape, while others are different. There are triangles, one square, and one parallelogram.

Exam Tip: Look for matching pairs among the pieces - knowing which shapes are identical helps you understand their relationships.

Question (b). What do you notice about the angles of each of the shapes?
Answer: In shapes 2, 3, and 6, only two angles are equal. In shapes 1, 5, and 4, all angles are equal (all angles are 60 degrees in the triangles and 90 degrees in the square). In shape 7 (the parallelogram), opposite angles are equal to each other, but the angles are not all the same.
In simple words: Some pieces have all equal angles, some have only two equal angles, and some have opposite angles equal.

Exam Tip: Different types of shapes have different angle patterns - triangles have three angles, quadrilaterals have four angles.

Question (c). What do you notice about the sides of each of the shapes?
Answer: In shapes 2, 3, and 6, only two sides are the same length. In shapes 1, 5, and 4, all sides are equal (equilateral triangles and a square). In shape 7 (the parallelogram), opposite sides are equal to each other, but not all sides are the same length.
In simple words: Some pieces have all sides equal, some have only two sides equal, and some have opposite sides equal.

Exam Tip: When shapes have equal sides, they also tend to have equal angles - look for this relationship in the tangram pieces.

Page 100

Which Shape Am I?

Question. Match the statements with appropriate shapes. Do some of them describe more than one shape?
Answer:

Statement 1: "All my angles are right angles, but all my sides are not equal" - Rectangle

Statement 2: "All my sides are equal, but all my angles are not" - Rhombus

Statement 3: "My opposite angles are equal, but my sides do not make a right angle" - Parallelogram

Statement 4: "Two pairs of sides are equal, but they do not make a right angle" - Kite or Parallelogram

Statement 5: "All my sides make right angles with each other and are equal" - Square

Statement 6: "My opposite angles are equal and so are my sides" - Rhombus or Square

Statement 7: "My opposite angles are equal and my sides make right angles" - Rectangle or Square

In simple words: Some statements describe only one shape, while others match with two or more different shapes.

Exam Tip: A square fits multiple descriptions because it is the most special quadrilateral - it has all the properties of rectangles, rhombuses, and parallelograms combined.

Page 101

Play with Circles

Question. Do you remember a circle? (a) Draw a circle with a compass and mark its centre. (b) Draw its diameter. Mark the endpoints of the diameter. (c) Draw another diameter of the circle and mark the endpoints. (d) Now join the four points.
Answer: When you connect the four endpoints of two diameters of a circle, you form a rectangle. The opposite sides and angles of this quadrilateral are equal. All angles are right angles (90 degrees).
In simple words: When you draw two diameters in a circle and connect their endpoints, you get a rectangle.

Exam Tip: Any two perpendicular diameters of a circle will always produce a rectangle because the circle ensures that the four points are positioned equally.

Question. What shape is formed? Check the sides of the quadrilateral and the angles obtained.
Answer: The shape formed is a rectangle. When you measure the sides, you will find that opposite sides are equal. When you measure the angles, you will find that all angles are right angles (90 degrees each).
In simple words: The shape is always a rectangle with opposite sides equal and all angles 90 degrees.

Exam Tip: A rectangle is defined by having all right angles and opposite sides equal - this activity proves that property.

Question. Try with a different pair of diameters. What do you notice about the shape that is formed?
Answer: Every time you draw two diameters and join their endpoints, you get a rectangle. No matter which pair of diameters you choose, the resulting shape is always a rectangle with equal opposite sides and all right angles.
In simple words: You always get a rectangle, no matter which diameters you use.

Exam Tip: This shows a key property - any quadrilateral formed by connecting the endpoints of two perpendicular diameters in a circle will always be a rectangle.

Question. Is it possible to create a 4-sided shape other than a rectangle through this process?
Answer: No, this process can only create a rectangle. The circle's geometry ensures that when you join the endpoints of any two diameters, you will always get a shape with four right angles and opposite sides that are equal - which is the definition of a rectangle. No other type of quadrilateral can be formed this way.
In simple words: This method only makes rectangles - you cannot make any other 4-sided shape.

Exam Tip: Understand the constraint - the circle's round shape and the diameter properties force the resulting shape to always be a rectangle.

Page 102

Cube Connections

Question 1. Here are three views of a cube. Can you draw them on the net in the correct order?
Answer: [Student activity - examine the three 3D views of a cube shown and draw the corresponding faces on a cube net in their correct positions, maintaining accurate orientation and relationships between faces]
In simple words: Look at how the cube faces appear in each view, then place them correctly on the flat net pattern.

Exam Tip: Remember that opposite faces of a cube cannot be next to each other on the net - they must be across from each other when folded.

Question 2. Here are some big solid cube frames. How many small cubes have been removed from each cube?
(a)
(b)
(c)
Answer: Count the number of empty spaces inside each frame cube.
(a) 7 cubes are removed.
(b) 32 cubes are removed.
(c) 81 cubes are removed.
In simple words: Look at each cube frame and find the holes or missing spaces inside it. Count how many small cubes have been taken away from the whole cube.

Exam Tip: Visualize the complete cube first, then identify which small cubes are missing by looking at the empty spaces shown in the frame.

Question 3. Nisha has glued 27 small cubes together to make a large solid cube. She paints the large cube red. How many of the original small cubes have - (a) three faces painted red? (b) two faces painted red? (c) one face painted red? (d) no faces painted red?
Answer:
(a) Three faces painted: 8 cubes. These are located at the corners of the big cube, where three faces meet.
(b) Two faces painted: 12 cubes. These sit along the edges but not at the corners. Each edge has 1 such cube in the middle, and there are 12 edges total, so 12 \( \times \) 1 = 12.
(c) One face painted: 6 cubes. These are found at the center of each face. Since there are 6 faces and each has 1 center cube, the count is 6 \( \times \) 1 = 6.
(d) No faces painted: 1 cube. This is the single cube positioned deep inside the large cube, completely hidden from the outside.
In simple words: When you paint a big cube made of 27 small cubes, the corner cubes get 3 colors, edge cubes get 2 colors, face-center cubes get 1 color, and the one cube right in the middle gets no paint at all.

Exam Tip: Always picture the 3 \( \times \) 3 \( \times \) 3 structure and identify each position type separately - corners have 8 positions, edges have 12, face centers have 6, and the core has 1.

Puzzle. Tanu arranged 7 shapes in a line. She used 2 squares, 2 triangles, 1 circle, 1 hexagon and 1 rectangle. Find her arrangement using the following clues: (a) The square is between the circle and the rectangle. (b) The rectangle is between the square and the triangle. (c) The two triangles are next to the square. (d) The hexagon is to the right of the triangle. (e) The circle is to the left of the square.
Answer:
(a) The square is between the circle and the rectangle: This means the order must be either Circle, Square, Rectangle or Rectangle, Square, Circle.
(b) The rectangle is between the square and the triangle: Now the sequence becomes Circle, Square, Rectangle, Triangle or Triangle, Rectangle, Square, Circle.
(c) The two triangles are next to the square: We already have one triangle after the rectangle. The other triangle must sit on the opposite side of the square. This gives us Triangle, Circle, Square, Rectangle, Triangle. However, from clue (e), the circle should be to the left of the square, so the arrangement is Triangle, Circle, Square, Rectangle, Triangle.
(d) The hexagon is to the right of the triangle: Our last shape is a triangle, so the hexagon goes after it. We still need to place one rectangle and one hexagon. The sequence now becomes Triangle, Circle, Square, Rectangle, Triangle, Hexagon.
(e) The circle is to the left of the square: This confirms Circle, Square in the order. We have now used both triangles, 1 circle, 1 hexagon, and 1 rectangle (2 squares were needed, but we have only used 1). We are missing one square! The only place it can fit is at the very end.

Final Arrangement (from left to right):
Triangle, Circle, Square, Rectangle, Triangle, Hexagon, Square
In simple words: Use the clues one by one to figure out where each shape must go. Keep checking each clue as you place shapes, and adjust when needed. The missing square goes at the end to complete the line.

Exam Tip: For logic puzzles, work through clues systematically and eliminate positions step by step. Write out each step of reasoning to avoid missing a shape or placing one twice.

Icosahedron and Dodecahedron

Question. What do these names mean? Once you count their faces, you will know.
Answer:
Icosahedron: An icosahedron is a three-dimensional solid with 20 faces. In its regular form, all these faces are shaped as equilateral triangles.
Dodecahedron: A dodecahedron is a three-dimensional shape with twelve flat faces. In its regular form, each of these twelve faces is an equal-sided pentagon.
In simple words: The name "icosa" means 20, so an icosahedron has 20 faces. The name "dodeca" means 12, so a dodecahedron has 12 faces.

Exam Tip: Remember the prefix: "icosa-" = 20 faces, "dodeca-" = 12 faces. This helps you recall the number of faces even if you forget which shape is which.

Question. What shapes do you see in an icosahedron and a dodecahedron?
Answer:
Icosahedron: All the faces are triangles. The solid looks as if it is built from many small pyramid shapes joined together.
Dodecahedron: All the faces are pentagons - five-sided shapes just like the black patches you see on a soccer ball.
In simple words: An icosahedron is made entirely of triangles. A dodecahedron is made entirely of five-sided pentagons.

Exam Tip: Visualizing the shape helps - imagine 20 tiny pyramid tips meeting at the center for an icosahedron, or soccer ball patches for a dodecahedron.

Question. Do all the faces look the same?
Answer:
Icosahedron: Yes, every single face is an identical triangle.
Dodecahedron: Yes, every single face is an identical pentagon.
In simple words: In both shapes, all faces are the same - no face is bigger or smaller or a different shape than the others.

Exam Tip: This property - having all identical faces - is what makes these "regular" polyhedra, and it is a key feature to mention when describing them.

Question. How many faces meet at a vertex (point)?
Answer:
Icosahedron: 5 triangles meet at each vertex.
Dodecahedron: 3 pentagons meet at each vertex.
In simple words: At each corner of an icosahedron, 5 triangle faces come together. At each corner of a dodecahedron, 3 pentagon faces come together.

Exam Tip: Counting faces at a vertex is easier if you trace one vertex on a model or picture and follow each face that touches it.

Question. Do the same number of faces meet at each vertex?
Answer:
Icosahedron: Yes, at every single corner, exactly 5 triangles meet.
Dodecahedron: Yes, at every single corner, exactly 3 pentagons meet.
In simple words: Both shapes are uniform - the number of faces at each corner never changes. This is what makes them "regular" solids.

Exam Tip: This uniformity across all vertices is a defining trait of Platonic solids and should be highlighted in your answer.

Question. How many edges do you see?
Answer:
The edge is the line where two faces meet.
Icosahedron: It has 30 edges.
Dodecahedron: It has 30 edges.
In simple words: An edge is where two flat faces join together in a line. Both shapes happen to have the same total number of edges - 30.

Exam Tip: Edges can be hard to count directly, so use the formula method (shown in the next question) to avoid making mistakes.

Question. How did you count them such that you do not miss out any edge or count an edge twice?
Answer:
For the Icosahedron: Each of the 20 triangles has 3 sides, giving us 20 \( \times \) 3 = 60. However, each edge is shared by exactly 2 triangles, so we counted every edge twice. The actual number of edges is 60 \( \div \) 2 = 30 edges.

For the Dodecahedron: Each of the 12 pentagons has 5 sides, giving us 12 \( \times \) 5 = 60. Again, each edge is shared by exactly 2 pentagons. So the number of edges is 60 \( \div \) 2 = 30 edges.
In simple words: Count the sides of all faces and add them together, but then divide by 2 because each edge borders two faces, not one.

Exam Tip: Always divide by 2 at the end - this corrects for the fact that every edge is counted twice (once from each neighboring face).

Question. Can you think of any other solid shapes that have faces that look the same?
Answer:
Yes, there are other solid shapes where all faces look identical:

Cube (or Hexahedron): All faces are identical squares.
Tetrahedron: A pyramid shape with 4 identical triangular faces.
Octahedron: Resembles two pyramids stuck base-to-base together. It has 8 identical triangular faces.

These five shapes - the Cube, Tetrahedron, Octahedron, Icosahedron, and Dodecahedron - are together called the Platonic Solids. Each one has the special property that all its faces are the same and meet uniformly at every corner.
In simple words: When all faces of a 3-D shape are identical and the same number of faces meet at every corner, it is a Platonic solid. There are exactly five of these special shapes.

Exam Tip: Memorize the five Platonic solids and their face types - cube (squares), tetrahedron (4 triangles), octahedron (8 triangles), icosahedron (20 triangles), dodecahedron (12 pentagons).

Question. Do the same number of faces meet at each common vertex?
Answer:
Yes, the same number of identical faces meet at every single vertex in each Platonic solid. This uniformity at all corners is one of the defining features that makes these shapes "Platonic" or "regular".
In simple words: In a Platonic solid, every corner looks the same - the same number of identical faces always come together at each corner.

Exam Tip: This property of vertex uniformity is what separates Platonic solids from other polyhedra and is always an important point in exam answers.

Question. You can also build some 3-D shapes using straws or ice-cream sticks and clay or play dough. Which shapes did you make?
Answer:
Using straws or ice-cream sticks and clay or play dough, you can construct:

Cubes and cuboids (shaped like a box).
Pyramids with a square base (called a square pyramid) or with a triangular base (called a tetrahedron).
Triangular prisms (shaped like a tent or a roofline).
In simple words: Straws form the edges and clay forms the corners. You can easily build cubes, boxes, pyramids, and tent-like shapes this way.

Exam Tip: When building with straws and clay, make sure all edges that should be equal length are actually equal - this helps the shape stay properly formed.