Class 5 Maths Mela Chapter 7 NCERT Solutions: Shapes and Patterns

NCERT Solutions Class 5 Maths Mela Chapter 7 Shapes and Patterns (2025-26)

1. Let us make paper mats.

Q. Write the steps of the pattern in your notebook for each row until it starts repeating.

Answer:

• Row 1: 1 under, 1 over, 1 under, 1 over, … (repeat)
• Row 2: 1 over, 1 under, 1 over, 1 under, … (repeat)
• Continue alternate patterns of weaving for each row, repeating once you reach the same sequence as Row 1.

2. Can you figure out how to make this mat?

Answer:

• Row 1: 2 over, 1 under, 2 over, 1 under, …
• Row 2: 2 under, 1 over, 2 under, 1 over, …
• Use two colors for alternate strips for clearer pattern, and repeat the process for further rows.

3. Tiling and Tessellation

Find Out: Can regular triangles fit together at a point without any gap? How many of them fit together?

Answer: Yes, regular triangles (equilateral triangles) can fit together at a point without any gap. Six equilateral triangles meet at a point.

Can squares (a regular 4-sided shape) fit together around a point without any gap or overlap? How many squares did you need?

Answer: Yes, squares can fit together around a point without any gaps or overlaps. Four squares fit around a point.

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 without gaps or overlaps because the total of their angles (each 90°) would be 450°, which is more than 360°, so they will overlap.

Can regular hexagons (6-sided shapes with equal sides) fit together around a point without any gaps or overlaps? Try and see. How many fit together at a point?

Answer: Yes, regular hexagons fit together at a point without any gaps or overlaps. Three regular hexagons fit together at a point (each angle is 120°, so 120° × 3 = 360°).

Do regular octagons fit together without any gaps or overlaps?

Answer: No, regular octagons do not fit together without gaps or overlaps. When placed together, there will be empty space between the shapes.

Here is a tessellating pattern with more than one shape. What shapes have been used in this pattern?

Answer: The shapes used in the tessellating pattern are squares and equilateral triangles.

4. Try This: How many different types of triangles can you make? What do you notice?

Answer: By joining two triangles, you can make: an isosceles triangle (two equal sides), an equilateral triangle (three equal sides), or a scalene triangle (no equal sides). Each isosceles triangle has two equal angles, the equilateral triangle has all equal angles, and the scalene triangle has all angles different.

Is it possible to make a triangle where all three sides are equal (equilateral triangle)?

Answer: Yes, it is possible to make a triangle with all three sides equal by joining appropriate pieces.

Is it possible to make a triangle where all three sides are unequal?

Answer: Yes, a triangle can be made where all sides are unequal — this is called a scalene triangle.

How many different 4-sided shapes (quadrilaterals) can you make?

Answer: By joining triangles, you can make different 4-sided shapes: parallelograms, rectangles, squares, and kites. For example, a kite has two pairs of adjacent equal sides, while parallelograms have opposite sides equal. Many quadrilaterals can be formed by rearranging the triangles.

What do you notice about the sides of a kite?

Answer: The kite has two pairs of adjacent sides that are equal. Side 1 equals Side 2, and Side 3 equals Side 4 (the adjacent pairs).

What types of angles do quadrilaterals A and B have? Which angles are equal in each of the above parallelograms?

Answer: In parallelogram A, the opposite angles are equal. In parallelogram B (rectangle), all angles are equal and are right angles. So, B is a rectangle—a special parallelogram.

Which of these shapes can be made with all 4 pieces? (a) Square (b) Rectangle (c) Triangle (d) Pentagon (e) Hexagon (f) Octagon

Answer: Using all 4 pieces, you can make: (a) Square, (b) Rectangle, (d) Pentagon (by arranging them), (e) Hexagon (with suitable placement). Triangle, and octagon cannot generally be made from four triangle pieces from the rhombus.

Which Shape Am I?

Cube Connections: 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—

• Three faces painted red? 8 cubes
• Two faces painted red? 12 cubes
• One face painted red? 6 cubes
• No faces painted red? 1 cube (the innermost cube)

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:

• The square is between the circle and the rectangle.
• The rectangle is between the square and the triangle.
• The two triangles are next to the square.
• The hexagon is to the right of the triangle.
• The circle is to the left of the square.

Answer: The arrangement is:
Circle – Square – Triangle – Rectangle – Triangle – Hexagon – Square

Icosahedron and Dodecahedron: What shapes do you see in an icosahedron and a dodecahedron?

Answer: An icosahedron has 20 equilateral triangle faces. A dodecahedron has 12 regular pentagon faces.

Do all the faces look the same?

Answer: Yes, all faces of an icosahedron are equal triangles, and all faces of a dodecahedron are equal pentagons.

How many faces meet at a vertex (point)?

Answer: In an icosahedron, five faces meet at a vertex. In a dodecahedron, three faces meet at a vertex.

Do the same number of faces meet at each vertex?

Answer: Yes, in both shapes, the same number of faces meet at each vertex—five for icosahedron and three for dodecahedron.

How many edges do you see?

Answer: An icosahedron has 30 edges. A dodecahedron also has 30 edges.

Understanding Shapes and Patterns – NCERT Class 5 Maths

Mastering NCERT Solutions Class 5 Maths Mela Chapter 7 Shapes and Patterns (2025-26) helps students recognize unique patterns, tessellations, and properties of 2D and 3D shapes. Developing a solid foundation here enhances both logical reasoning and exam performance.

Focus on drawing grids, exploring tessellations, and building solids using everyday materials. Practicing these exercises boosts visualization skills and prepares you for school tests with confidence and creativity.

Revise concepts on triangles, quadrilaterals, and patterns regularly. Challenge yourself with puzzles and shape arrangements to sharpen mathematical thinking. Keep practicing for better retention and high exam marks!