## Chapter 11 Perimeter and Area Exercise 11.1

Question 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 m2 of the land costs ₹ 10,000.

Given
Length of rectangular land = 500 m
Breadth of rectangular land = 300 m
To find = Area
Cost of land

(i) Area of rectangle = l x b
= 500 x 300
= 150000 m²
Therefore, the area of the rectangular land is 150000 m².

(ii) Area of rectangular land = 150000 m²
Cost of 1 m² land = ₹ 10000
Cost of 150000 m² land = ?
= 10000 x 150000
= ₹ 1,50,00,00,000
Therefore, the cost of the land is ₹ 1,50,00,00,000.

Question 2: Find the area of a square park whose perimeter is 320 m.
Given
Perimeter of a square park = 320 m
To find - Side length
Area
Side = perimeter/4
= 320/4
= 80 m
Therefore, the length of each side is 80 m.
Area of Square = side x side
= 80 x 80
= 6400 m²
Therefore, the area of square park is 6400 m².

Question 3: Find the breadth of a rectangular plot of land, if its area is 440 m2 and the length is 22 m. Also find its perimeter.
Given
Area of rectangular plot = 440 m²
Length of rectangular plot = 22 m
Perimeter
= 440/22
= 20 m
Therefore, the breadth of the rectangular plot is 20 m.
Perimeter of a rectangle = 2 x (l + b)
= 2 x (22 + 20)
= 2 x 42
= 84 m
Therefore, the perimeter of the rectangular plot is 84 m.

Question 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 rectangular sheet = 35 cm
Area
Perimeter of rectangle = 2 x (l + b)
100 = 2 x (35 + b)
100 = (2 x 35) + (2 x b)
100 = 70 + 2b
2b = 100 - 70 = 30
2b = 30
b = 30/2
b = 15 m
Therefore, the breadth of the rectangular sheet is 15 m.
Area of rectangle = l x b
= 35 x 15
= 525 m²
Therefore, the area of rectangular sheet is 525 m².

Question 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
Area of Square park = Area of rectangular park
Length of side of square park = 60 m
Length of rectangular park = 90 m
To find = Area
Area of square = side x side
= 60 x 60
= 3600 m²
= 3600/90
= 40 m
Therefore, the breadth of rectangular park is 40 m.

Question 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 rectangle = 40 cm
Breadth of rectangle = 22 cm
To find = Perimeter
Side of square
Which shape encloses more area
Perimeter of rectangle = 2 x (l + b)
= 2 x (40 + 22)
= 2 x 62
= 124 cm
Therefore, the perimeter of rectangle is 124 cm.
Perimeter of Square = Perimeter of Rectangle
Length of side of square = perimeter/4
= 124/4
= 31 cm
Therefore, the length of side of square is 31 cm.
Area of rectangle = length x breadth
= 40 x 22
= 880 cm²
Area of square = side x side
= 31 x 31
= 961 cm²
Compare
880 cm² < 961 m²
Therefore, square encloses more area.

Question 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 rectangle = 130 m
To find = Length
= Area
Perimeter of rectangle = 2 x (l + b)
130 = 2 x (l + 30)
130 = (2 x l) + (2 x 30)
2l = 130 - 60
2l = 70
l = 70/2
l = 35
Therefore, length of a rectangle is 35 cm.
Area of rectangle = l x b
= 35 x 30
= 1050 cm²
Therefore, the area of rectangle is 1050 cm².

Question 8: A door of length 2 m and breadth 1 m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m. Find the cost of white washing the wall, if the rate of white washing the wall is ₹ 20 per m
².

Given
Length of wall = 4.5 m
Breadth of wall = 3.6 m
Door length = 2 m
Rate of white washing = ₹ 20 per m²
To find = Area to be white washed
= Cost of white washing
Area of rectangle = l x b
= 4.5 x 3.6
= 16.2 m²
Therefore, the area of wall = 16.2 m².
Area of rectangle = l x b
= 2 x 1
= 2 m²
Therefore, the area of door is 2 m².
Area to be white washed = area of wall - area of door
= 16.2 m² - 2 m²
= 14.2 m²
Therefore, the area to be white washed is 14.2 m².
Cost of white washing 1 m² = ₹ 20
Cost of white washing 14.2 m² = ?
= 20 x 14.2
= ₹ 284
Therefore, the cost of white washing the wall is ₹ 284.