11. Grandmother’s Quilt

The quilt has 15 patches along the length and 10 patches along the breadth.

Border = 15 + 10 + 15 + 10 = 50 units.

So, (ii) Green lace — 50 units will cover the entire border.

The border is 50 units. She can use 25 units of blue lace and 25 units of red lace.

Blue lace covers one length and one breadth (15 + 10 = 25). Red lace covers the other two sides.

Pentagon: 5 sides of 4 cm. Perimeter = 5 × 4 = 20 cm

Two triangles joined at a point: 6 sides of 5 cm. Perimeter = 6 × 5 = 30 cm

Length + Breadth must be half of the perimeter.

(a) 26 ÷ 2 = 13. Rectangles: 8 cm × 5 cm and 9 cm × 4 cm (or 10 cm × 3 cm).

(b) 18 ÷ 2 = 9. Rectangles: 5 cm × 4 cm and 6 cm × 3 cm (or 7 cm × 2 cm).

There are 6 rows with 15 patches in each row.

6 × 15 = 90 patches

They found that triangle, square and rectangle shapes cover the top of the table without gaps and overlaps. Circle shape leaves gaps.

20 triangles cover Table 1. 8 squares cover Table 3. 3 rectangles cover Table 4.

Circles do not tile. They leave gaps, so we cannot use them to measure area.

The area of Table 1 is 20 triangle units. The area of Table 3 is 8 square units. The area of Table 4 is 3 rectangle units.

Rectangular objects like notebooks, pencil boxes and Maths textbooks cover the table without gaps. Round lunch boxes leave gaps.

The desk has 9 × 6 = 54 squares.

(a) Green triangles (each is half a square): 54 × 2 = 108

(b) Red triangles (each covers 4½ squares): 54 ÷ 4½ = 12

(c) Blue squares: 54

On the square grid: A = 3 × 4 = 12 squares, B = 2 × 4 = 8 squares, C = 2 × 5 = 10 squares.

A is larger than B. C is larger than B. A is larger than C.

Rectangle A has the largest area.

Area of Garden A = 2 × 5 = 10 cm square

Area of Garden B = 4 × 3 = 12 cm square

Garden B has a larger area, though Garden A looks longer.

(a) 5 patches × 2 rows. Area = 10 square units. Perimeter = 5 + 2 + 5 + 2 = 14 units.

(b) 4 patches × 3 rows. Area = 12 square units. Perimeter = 4 + 3 + 4 + 3 = 14 units.

The mats need a different number of patches, though their perimeters are the same.

No, it is not always true.

For example, a 1 × 6 rectangle has area 6 and perimeter 14. A 3 × 3 square has a bigger area (9), but a smaller perimeter (12).

Shapes (a), (b), (c), (d) and (f) have the same area of 12 sq cm, but their perimeters are different.

So, shapes with the same area can have different perimeters.

(a) and (b) have the same perimeter (12 cm). (c), (d) and (e) have the same perimeter (16 cm).

All five shapes have the same area of 7 sq cm. Even with the same area, the perimeters are not the same.

The given shape is 9 cm × 2 cm. Area = 18 sq cm, perimeter = 22 cm.

All have the same area, but different perimeters. The shape closer to a square has the smallest perimeter.

No. Both have the same area.

Shape (a) is a 3 × 3 square = 9 square units.

Cut triangle (b) along its middle line. The two halves fit together to make a 3 × 3 square. So, its area is also 9 square units.

There are 6 rows of 4 patches each. 6 × 4 = 24 patches.

Area of rectangle = Length × Breadth = 6 cm × 4 cm = 24 square cm.

Example: If the classroom is 8 m long and 6 m wide,

Area = 8 m × 6 m = 48 square m

Perimeter = 2 × 8 m + 2 × 6 m = 28 m

Area = 42 m × 34 m = 1,428 square m

Breadth = Area ÷ Length = 64 ÷ 16 = 4 m

The figure is a rectangle 32 cm long. Its height is 6 cm + 12 cm = 18 cm.

Area = 32 cm × 18 cm = 576 square cm

(Or: 32 × 6 + 32 × 12 = 192 + 384 = 576 square cm)