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

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Ex 11.1 are the part of NCERT Solutions for Class 7 Maths. Here you can find the NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Ex 11.1.

Ex 11.1 Class 7 Maths 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: Length of the land, l = 500 m, Breadth of the land, b = 300 m
(i) Area of the land = l × b
= 500 m × 300 m = 1,50,000 m²
(ii) Cost of the land = ₹ 10,000 × 150000 = ₹ 1,50,00,00,000

Ex 11.1 Class 7 Maths Question 2.

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

Solution:
Given: Perimeter of the square park = 320 m
Side of the square park = Perimeter ÷ 4
= 320/4 m = 80 m
Area of the square park = Side × Side
= 80 m × 80 m = 6400 m²

Ex 11.1 Class 7 Maths 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 of the rectangular plot = 440 m²
Length of the plot = 22 m
Breadth of the plot = Area ÷ Length = 440/22 = 20 m
Perimeter of the plot = 2[l + b] = 2[22 m + 20 m]
= 2 × 42 m = 84 m

Ex 11.1 Class 7 Maths Question 4.

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

Solution:
Given: Perimeter of the rectangular sheet = 100 cm
Length of the sheet = 35 cm
Perimeter of a rectangle = 2(l + b)
100 = 2(35 + b)
100/2 = 35 + b
⇒ 50 = 35 + b
⇒ b = 50 – 35 = 15 cm
∴ Breadth of the sheet = 15 cm
Area of the sheet = l × b = 35 cm × 15 cm
= 525 cm²

Ex 11.1 Class 7 Maths Question 5.

The area of a square park is 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.

Solution:
Given: Side of the square park = 60 m

Length of the rectangular park = 90 m

Let the breadth of the rectangular park be b.

Area of the rectangular park = Area of the square park
90 × b = 60 × 60
⇒ 90 × b = 3600

⇒ b = 3600/90
⇒ b = 40 m
Hence, the breadth of the rectangular park is 40 m.

Ex 11.1 Class 7 Maths 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 of the rectangle = 40 cm, Breadth of the rectangle = 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 the shape of a square.
Perimeter of the square = 124 cm
⇒ 4 × side = 124
∴ Side = 124/4 cm = 31 cm
So, the measure of each side of the square is 31 cm.
Area of the rectangular shape = l × b
= 40 cm × 22 cm
= 880 cm²
Area of the square shape = (Side)²
= (31)² = 961 cm²
Since, 961 cm² > 880 cm²
Hence, the square shape encloses more area.

Ex 11.1 Class 7 Maths 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.

Solution:
Given: Perimeter of the rectangle = 130 cm
Breadth of the rectangle = 30 cm
Perimeter of the rectangle = 2(l + b)
130 = 2(l + 30)
⇒ 130/2 = l + 30
⇒ 65 = l + 30
⇒ l = 65 – 30
∴ l = 35 cm
Area of the rectangle = l × b = 35 cm × 30 cm
= 1050 cm²

Ex 11.1 Class 7 Maths 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 the 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

Area of the door = l × b = 2 m × 1 m = 2 m²
∴ Area of the wall to be whitewashed = Area of the wall – Area of the door
= 16.20 m² – 2 m²= 14.20 m²
Cost of whitewashing = ₹ 20 × 14.20 = ₹ 284.00
Hence, the required cost of whitewashing is ₹ 284.