Class 5 Mathematics

Chapter 11 Solutions — Grandmother's Quilt

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Solutions

Overview

Step-by-step NCERT solutions for Grandmother's Quilt (Chapter 11, NCERT Class 5 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Grandmother's Quilt textbook chapter.

Solved

What these solutions cover

All 28 questions in Grandmother's Quilt are solved in the PDF. Here's what's inside, exercise by exercise:

Opening Activity — Quilt Border and Perimeter (p. 142)

1.
Grandmother wants to decorate the entire border of her quilt with lace. Tick the lace option that would cover the entire border.
- (i) Red lace — 40 units
- (ii) Green lace — 50 units
- (iii) Blue lace — 25 units
Grandmother decides to use TWO different coloured laces. How much lace of each kind will be needed to cover the entire border?

Let Us Do — Perimeter of Shapes (p. 142)

1.
Find the perimeter of the following shapes. All sides of the following shapes are equal.
- (a) A pentagon (5-sided shape) with each side = 4 cm.
- (b) A hexagon-like shape with each side = 5 cm.
2.
Draw two rectangles each having the following perimeters.
- (a) 26 cm
- (b) 18 cm

Tiling and Area — Rug Patches and Table Covering (p. 143)

Grandmother is making a rug with square patches. The picture shows the rug. How many patches have they used to make it?
Preetha and Adrit cover their table tops with different shapes. Looking at Tables 1, 2, 3, and 4: — Which shapes cover the top without gaps and overlaps? — Which shape leaves gaps? — How many triangles cover Table 1? — How many squares cover Table 3? — How many rectangles cover Table 4? — What is the area of Table 1 in triangle units, Table 3 in square units, Table 4 in rectangle units?
3.
Now try to cover the top of YOUR table without gaps and overlaps with the following objects of the same size:
- (a) Notebooks,
- (b) Lunch boxes,
- (c) Pencil boxes,
- (d) Maths textbooks. Which of the above objects covered the region completely?

Let Us Do — Tiles on a Desk (p. 144)

1.
Preetha covers her desk (the grid is 9 units wide x 6 units tall = 54 square units) with different tile shapes as shown. How many of each shape will cover the desk?
- (a) Green triangles (each = a small right triangle made from half a 1 unit x 1 unit square, area = 1/2 sq unit)
- (b) Red triangles (each = a right triangle with legs 3 units x 3 units, area = 4 1/2 sq units)
- (c) Blue squares (each = 1…

Comparing Shapes

Three rectangles A (yellow), B (pink), and C (purple) are placed on a square grid (1 unit = 1 cm). Which rectangle has the largest area? Compare A and B, B and C, and A and C.

Let Us Do — Area of Gardens on Square Grid (p. 145–146)

Compare the areas of the two gardens on the square grid (each small square = 1 cm). Garden A and Garden B are shown on the same grid. Find: Area of Garden A = ___ cm square Area of Garden B = ___ cm square
Trace your palm on the square grid and find the approximate area of your palm. Compare it with your friend's palm. Who has a bigger palm?
3.
Collect leaves of different kinds. Put them on a square grid and find their area.
- (a) Name the leaf with the largest area.
- (b) Name the leaf with the smallest area.
The following mats are made of square patches of equal size. How many square patches will be required to cover each mat? Would both mats require an equal or different number of patches? (Trace the small square patch shown and use it to measure each mat.)
Trisha makes two rectangles. She says: 'I increased the area of my rectangle, and the perimeter increased.' Do you think this is always true?

Let Us Explore

1.
Tick the shapes (a)–(f) on the square grid (1 cm squares) that have the same area. Find the perimeters of those shapes. What do you notice? Discuss.
- (a) Horizontal rectangle: 5 wide x 2 tall
- (b) L-shaped: ~6 sq cm
- (c) L-shape: ~8 sq cm
- (d) Rectangle: 4 wide x 2 tall
- (e) Thin strip: 1 wide x 6 tall
- (f) Long strip: 1 wide x 10 tall
2.
Tick the shapes (a)–(e) on the square grid that have the same perimeter. Find the areas of those shapes. What do you notice? Discuss.
- (a) 2x2 square
- (b) T-shaped or cross shape
- (c) L-shaped or staircase
- (d) Vertical L-shape
- (e) Horizontal bar

Let Us Do

Shape (a) is a green rectangle 7 cm wide x 2 cm tall on the square grid. Draw different shapes having the SAME area as shape (a). Write the perimeter of each. What do you notice?
2.
Is the area of shape
- (a) less than the area of shape
- (b) given below?
- (a) A blue square on the grid: 3 cm x 3 cm.
- (b) A downward-pointing orange triangle on the grid: base = 6 cm, height = 3 cm. Discuss.

Area Formula for Rectangles and Squares (p. 150–151)

Grandmother's patchwork rectangle has 6 rows of 4 patches each. How many patches does she need? Verify using Area = Length x Breadth.
A square has sides 5 cm long. Find its area and perimeter.

Let Us Do — Area and Perimeter with Formula (p. 151–153)

Find the area of your classroom floor in square metres. Take the help of your teacher to measure the length and breadth of the floor. What is the perimeter of the classroom floor?
2.
Find the area and perimeter of the following shapes on the square grid (1 cm per square). All shapes are rectangles (or squares).
- (a) Square: 6 cm wide x 6 cm tall
- (b) Rectangle: 4 cm wide x 7 cm tall
- (c) Rectangle: 12 cm wide x 4 cm tall
- (d) Square: 3 cm wide x 3 cm tall
- (e) Rectangle: 6 cm wide x 5 cm tall
Find the area and perimeter of the following objects by measuring them with a scale or measuring tape. Fill in the table. 1. Cover of the Notebook 2. Newspaper 3. Blackboard 4. Ludo board 5. (Your choice) 6. (Your choice)
Find the area of a rectangular field whose length is 42 m and breadth is 34 m.
The area of a rectangular garden is 64 square m and its length is 16 m. What is its breadth?
Find the area of the figure below. The figure is a rectangle whose total width is 32 cm. Its height is marked in two parts: 6 cm and 12 cm.

Let Us Play — Tile Perimeter Game (p. 154)

In the tile game, players roll a die and add square tiles (each side = 1 unit) to build a shape. The example in the book shows a shape with perimeter labelled as 10. Find the perimeter of the tile shape shown (a connected arrangement of square tiles with all edge lengths labelled as 1).
In the game, Player 1 rolls the die and places tiles. Player 2 then adds tiles to the same figure. The goal is for the combined shape to reach a perimeter of 24. The book shows an intermediate stage with perimeter = 12. Explain how adding more tiles can reach perimeter = 24.

Sample

Worked examples

3 questions from Grandmother's Quilt, solved step by step.

Opening Activity — Quilt Border and Perimeter (p. 142)

Grandmother decides to use TWO different coloured laces. How much lace of each kind will be needed to cover the entire border?

The quilt border is 50 units long.

Use Blue lace (25 units) for two shorter sides and Red lace (25 units) for the remaining two longer sides.

25 + 25 = 50 units total — exactly covers the border.

So: 25 units of Blue lace + 25 units of Red lace.

Answer: 25 units of Blue lace + 25 units of Red lace = 50 units total, covering the entire border.

Let Us Do — Perimeter of Shapes (p. 142)

Find the perimeter of the following shapes. All sides of the following shapes are equal. (a) A pentagon (5-sided shape) with each side = 4 cm. (b) A hexagon-like shape with each side = 5 cm.

(a) Pentagon: 5 sides, each 4 cm.

Perimeter = 5 x 4 = 20 cm.

(b) The shape has 6 equal sides, each 5 cm.

Perimeter = 5 + 5 + 5 + 5 + 5 + 5 = 6 x 5 = 30 cm.

Answer: (a) 20 cm (b) 30 cm

Comparing Shapes

Three rectangles A (yellow), B (pink), and C (purple) are placed on a square grid (1 unit = 1 cm). Which rectangle has the largest area? Compare A and B, B and C, and A and C.

Count the squares each rectangle covers on the grid:

Rectangle A (yellow) = 3 wide x 4 tall = 12 square units.

Rectangle B (pink) = 2 wide x 4 tall = 8 square units.

Rectangle C (purple) = 2 wide x 5 tall = 10 square units.

A (12) > B (8): Rectangle A has a larger area than B.

C (10) > B (8): Rectangle C has a larger area than B.

A (12) > C (10): Rectangle A has the largest area among all three.

Answer: A = 12 sq units, C = 10 sq units, B = 8 sq units. Rectangle A has the largest area.

All 28 questions in Grandmother's Quilt are solved step by step in the Solutions PDF above.

Keep solving

Chapter 11 Solutions — Grandmother's Quilt

Overview

What these solutions cover

Opening Activity — Quilt Border and Perimeter (p. 142)

Let Us Do — Perimeter of Shapes (p. 142)

Tiling and Area — Rug Patches and Table Covering (p. 143)

Let Us Do — Tiles on a Desk (p. 144)

Comparing Shapes

Let Us Do — Area of Gardens on Square Grid (p. 145–146)

Let Us Explore

Let Us Do

Area Formula for Rectangles and Squares (p. 150–151)

Let Us Do — Area and Perimeter with Formula (p. 151–153)

Let Us Play — Tile Perimeter Game (p. 154)

Worked examples

Grandmother decides to use TWO different coloured laces. How much lace of each kind will be needed to cover the entire border?

Find the perimeter of the following shapes. All sides of the following shapes are equal. (a) A pentagon (5-sided shape) with each side = 4 cm. (b) A hexagon-like shape with each side = 5 cm.

Three rectangles A (yellow), B (pink), and C (purple) are placed on a square grid (1 unit = 1 cm). Which rectangle has the largest area? Compare A and B, B and C, and A and C.

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