Page 225 - ICSE Math 8

Breadth of the field excluding the path = 15 m – 3 m – 3 m = 9 m

Area of the field excluding the path = 18 m × 9 m = 162 m 2
2
2
∴ Area of the path = 360 m – 162 m = 198 m 2
Area and Perimeter of a Square D C

2
2
2
If the length of a side of a square is a units, then its area is (a × a) unit , or a unit .
Perimeter of square = Sum of the lengths of its sides = 4a d
If d be the length of the diagonal AC of square ABCD, then d = 2 a
2
Example 3: The area of a square is 32 cm . Find its perimeter and its length of the A B
diagonal. a
Solution: Let the length of a side of the square be a cm. Try These
Area of the square = 32 cm 2
1. Find the diagonal of a rectangle
2
2
⇒ a = 32 ⇒ a = 32 = 4 2 with length 12 m and area 60 m .
Perimeter of a square = 4a = 4 × 4 2 cm = 16 2 cm 2. Find the diagonal of a square with
2
area 81 cm .
Length of the diagonal = 2 a = 2 × 4 2 cm = 8 cm
Example 4: In the middle of a square garden of side 80 m, there are two straight 38 m
paths at right angle to each other which divide the park into 4 square 4 m
regions. If the straight paths are 4 m wide, find the area of the two
paths. (80 – 4) 4 m 4 m
Solution: Side of each square region = 2 m = 38 m 38 m 4 m
Area of each square region = 38 m × 38 m = 1,444 m 2
Area of the square garden = 80 m × 80 m = 6,400 m 2 80 m
∴ Area of the two paths = Area of the square garden – 4(Area of the square region)
2
2
= 6,400 m – 4(1,444 m )
2
= 6,400 m – 5,776 m 2
= 624 m 2

EXERCISE 21.1

2
1. The area of a rectangle is 84 cm and its breadth is 12 cm. Find its length and perimeter.
2. The perimeter of a square is 144 cm. Find its area.

3. The diagonal of a square plot is 6 2 m long. Find its perimeter and area.
4. The length of the diagonal of a rectangle is 15 cm. Find its length and area, if its breadth is 9 cm.
5. The ratio of the length and breadth of a rectangular park is 5 : 3. If the area of the park is
2
2,940 m , find the cost of fencing the boundary of the park at the rate of ` 8 per metre.
6. The length of a rectangle is 30 cm and its perimeter is equal to the perimeter of a square with side 24 cm.
Find the breadth and area of the rectangle.

7. A path of uniform width 2.5 m runs outside a rectangular plot of dimension 32 m by 18 m. Find the area
of the path.
8. Outside a square field of side 250 m, there is a path of width 3 m. Find the cost of paving the path at the
rate of ` 3.50 per metre square.
9. A rectangular hall is 20 m long and 18 m wide. Its floor is to be covered with square tiles each of side
15 cm. Find the cost of the tiles required at the rate of ` 6 per tile.

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