Chapter 11 Perimeter and Area Exercise 11.1

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
Solution:
Given: l = 500 m, b = 300 m
(i) Area = l × b
= 500 m × 300 m = 150000 m²
(ii) Cost of land = ₹ 10,000 × 150000 = ₹ 15,00,000,000

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.
Solution:
Given: Area = 440 m²
Length = 22 m

Perimeter = 2[l + b] = 2 [22 m + 20 m]
= 2 × 42 m = 84 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?
Solution:
Given: Length = 40 cm, Breadth = 22 cm Perimeter of the rectangle
= Length of the wire
= 2(l + b) = 2(40 cm + 22 cm)
= 2 × 62 cm = 124 cm
Now, the wire is rebent into a square.
Perimeter = 124 cm
⇒ 4 × side = 124

So, the measure of each side = 31 cm
Area of rectangular shape = l × b
= 40 cm x 22 cm
= 880 cm²
Area of square shape = (Side)²
= (31)² = 961 cm²
Since 961 cm² > 880 cm²
Hence, the square encloses more area.

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 m².
Solution:
Given: Length of wall = 4.5 m
Breadth of the wall = 3.6 m
Length of the door = 2 m
Breadth of the door = 1 m
Area of the wall = l × b = 4.5 m × 3.6 m = 16.20 m²
= 16.20 m²

Area of the door = l × b = 2 m × 1 m = 2 m²
∴ Area of the wall to be white washed = Area of the wall – Area of the door
= 16.20 m² – 2 m²= 14.20 m²
Cost of white washing
= ₹ 14.20 × 20 = ₹ 284.00
Hence, the required area = 14.20 m² and the required cost = ₹ 284

Exercise 11.2

Exercise 11.3

Exercise 11.4