# NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Ex 11.1

These NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Ex 11.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths 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.
(i) Length of the rectangular piece
(1) = 500 m
(b) = 300 m
Area = 1 × b sq. unit
= 500 × 300 m2
= 150000m2

(ii) Cost of the land = ₹ 150000 × 10, 000
= ₹ 1,50,00,00,000

Question 2.
Find the area of a square park whose perimeter is 320 m.
Perimeter of the square park = 320 m
4 × side = 320
side = $$\frac{320}{4}$$ = 80 m
Area of the square park = side × side = 80 × 80 m2
= 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.
Length of the rectangular plot = 22 m
Area of the rectangular plot = 440 m2
1 × b = 440
22 × b = 440
b = $$\frac{440}{22}$$ = 20m
Breadth of the rectangle = 20 m
Perimeter of the rectangular plot = 2 (l + b)
= 2(22 + 20) m
= 2 × 42 = 84 m
∴ 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.
Ans: Length of the rectangular sheet (1) = 35
Perimeter of the rectangular sheet = 100 cm
2(1 + b) = 100
2(35+ b) = 100
70 + 2b = 100
2b = 100 – 70
2b = 30 , 30
b = $$\frac { 30 }{ 2 }$$ = 15 cm
Area of the rectangular sheet
= 1 × b sq. units
= 35 × 15 cm2
= 525 cm2
Thus,
(i) Breadth of the rectangular sheet = 15 cm
(ii) Area of the rectangular sheet = 525 cm2

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.
Side of the square park = 60 m
Area of the square park = 60 × 60 m2
= 3600 m2
Length of the rectangular park = 90 m
Area of the rectangular Park
= Area of the square park = 3600 m2
1 × b = 3600
90 × b = 3600
b = $$\frac { 3600 }{ 90 }$$
= 40 m
∴ Breadth of the rectangular park = 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?

Length of the wire
(l) = 40 cm
(b) = 22 cm

Area of the rectangle = 1 × b
= 40 × 22 cm2
= 880 cm2

Perimeter of the rectangular wire = 2(1 + b)
= 2(40 + 22)cm
= 124 cm.

Perimeter of the square = Perimeter of the rectangle
4 × side = 124
side = $$\frac{124}{4}$$ = 31 cm
Side of a square =31 cm
Area of the square = 31 × 31 cm2
= 961 cm2
961 cm2 > 880 cm2
Area of the square is more than the area of rectangle.

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.
Breadth of the rectangle (b) = 30 cm
Perimeter of a rectangle =130 cm
2 (l + b) = 130 cm
2(l + 30) = 130
2l + 60 = 130
2l = 130 – 60
2l = 70
l = $$\frac{70}{2}$$ = 35cm
Length of the rectangle = 35 cm
Area of the rectangle = l × b sq units = 35 × 30 cm2
= 1050 cm2
∴ Area of the rectangle

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.

Length of the wall (l) = 4.5 m
Breadth of the wall (b) = 3.6 m
∴ Area of the wall = l × b sq. units
= 4.5 × 3.6 m2
= $$\frac{45}{10} \times \frac{36}{10}$$ m2
= $$\frac{1620}{100}$$ m2
= 16.2 m2
Area of the door = 2 m × 1 m
(l = 2 m, b = 1 m) = 2 m2
Area to be white washed =
Area of the wall – Area of the door
= 16.2 m2 – 2 m2
= 14.2 m2
Rate of white washing per m2 = ₹ 20
∴ Cost of while washing = ₹ 20 × 14.2
= ₹ 284

error: Content is protected !!