# Perimeter and Area

## Exercise 11.1

1). The length and the breadth of a rectangular piece of land are 500 m and 300 m respectively. Find

(i) its area (ii) the cost of the land, if 1 m^{2} of the land costs 10,000.

Given: length of the rectangular land = 500 m

Breadth of the rectangular land = 300 m

Rate of the land = 10000

Area of the land = length X breadth

= 500 X 300

= 150000 m^{2}

The cost of the land = Rate X Area

= 10000 X 150000

= ₹ 1500000000

Ans: area of the land = 150000 m^{2}

Cost of the land = ₹ 1500000000

2). Find the area of a square park whose perimeter is 320 m.

Given: Perimeter of the square = 320 m

Perimeter of the square = 4 X side

4 X side = 320

Length = (320)÷ 8

= 40 m

Area of the square = side X side

= 40 X 40

= 1600 m^{2}

Ans: area of the square = 1600 m^{2}

3). Find the breadth of a rectangular plot of land, if its area is 440 m^{2} and the length is 22 m. Also find its perimeter.

Given: length of the rectangular plot = 22 m

Area of the plot = 440 m^{2}

To Find: breadth of the rectangular plot = ?

Perimeter = ?

Area of the plot = length X breadth

440 = 22 X breadth

22 X breadth = 440

breadth = 440 ÷ 22

breadth = 20

perimeter = 2 (length + breadth)

= 2 (22 + 20)

= 2 X 42

= 84 m.

Ans: breadth of the rectangular plot = 20 m

Perimeter of the rectangular plot = 84 m.

4). The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.

Given: perimeter of rectangular sheet = 100 cm

Length of the sheet = 35 cm

To find: breadth of the sheet = ?

Area of the sheet = ?

Perimeter of the sheet = 100

2(length + breadth) = 100

2(35 + breadth) = 100

35 + breadth = 100 ÷ 2

35 + breadth = 50

Breadth = 50 – 35

breadth = 15 cm

area of the sheet = length X breadth

= 35 X 15

= 525 sq cm.

Ans: breadth of the sheet = 15 cm

Area of the sheet = 525 sq cm

5). The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

Given: side of the square park = 60 m

Length of the rectangular park = 90 m

Area of the square park = area of the rectangular park

To find: breadth of the rectangular park = ?

Area of the square park = area of the rectangular park

Side^{2} = length X breadth

60^{2} = 90 X breadth

90 X breadth = 60^{2}

breadth = 3600 ÷ 90

breadth = 40

Ans: breadth to the rectangular park = 40 m

6). A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?

Given: length of the rectangle = 40 cm

breadth of the rectangle = 22 cm

perimeter of rectangle = perimeter of the square

To find: side of the square = ?

Which shape has more area

Perimeter of the square = perimeter of the rectangle

4 X side = 2(length + breadth)

4 X side = 2(40+22)

4 X side = 2 X 62

4 X side = 124

Side = 124 ÷ 4

side = 31 cm

area of square = sideX side

= 31 X 31

= 961 sq cm

area of the rectangle = length X breadth

= 40 X 22

= 880 sq cm

Area of the square > area of the rectangle

Ans: side of the square = 31 cm

square shape encloses more area

7). The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30 cm, find its length. Also find the area of the rectangle.

Given: perimeter of a rectangle = 130 cm

breadth of the rectangle = 30 cm

To find: length of the rectangle = ?

area of the rectangle = ?

perimeter of rectangle = 130

2(length + breadth) = 130

2(length + 30)= 130

length + 30 = 130 ÷ 2

length = 65 – 30

length = 35 cm

area of the rectangle = length X breadth

= 35 X 30

= 1050 sq cm

Ans: length of the rectangle = 35 cm

area of the rectangle = 1050 sq cm

8). A door of length 2 m and breadth 1m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m (Fig11.6). Find the cost of white washing the wall, if the rate of white washing the wall is ₹ 20 per m^{2}.

Given: length of the wall = L = 4.5 m

breadth of the wall = B = 3.6 m

length of the door = l = 2 m

breadth of the door = b = 1 m

rate of whitewashing the wall = ₹ 20 per m^{2}

to find: cost of whitewashing the wall = ?

area of white washing the wall = area of the wall – area of the door

area of the wall = length X breadth

= 4.5 X 3.6

= 16.2 m^{2}

area of the door = length X breadth

= 2 X 1

= 2 m^{2}

area of white washing the wall = area of the wall – area of the door

= 16.2 – 2

= 14.2 m^{2}

Cost of white washing = Rate X area

= 20 X 14.2

= ₹ 284

Ans: Cost of whitewashing the wall = ₹ 284

Click here for the solutions of