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

NCERT Solutions Class 7 Mathematics 
Chapter – 11 (Perimeter and Area)

The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 11 Perimeter and Area Exercise 11.1 has been provided here to help the students in solving the questions from this exercise. 

Chapter : 11 Perimeter and Area

• NCERT Solution Class 7 Maths Exercise – 11.2
• NCERT Solution Class 7 Maths Exercise – 11.3
• NCERT Solution Class 7 Maths Exercise – 11.4

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 m² of the land costs ₹ 10,000.

Solution –
Given that,
Length of the rectangular piece of land = 500 m
Breadth of the rectangular piece of land = 300 m

(i) Area of rectangle = Length × Breadth
= 500 × 300
= 150000 m²

(ii) Cost of the land for 1 m² = ₹ 10000
Cost of the land for 150000 m² = 10000 × 150000
= ₹ 1,50,00,00,000

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

Solution –
Given that,
Perimeter of the square park = 320 m
4 × Length of the side of park = 320 m
Length of the side of park = = 80 m
So, Area of the square park = (length of the side of park)²
= (80m)²
= 6,400 m²

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 that,
Area of the rectangular plot = 440 m²
Length of the rectangular plot = 22 m
Area of the rectangle = Length × Breadth
440 = 22 × Breadth
Breadth =
Breadth = 20 m
Then,
Perimeter of the rectangle = 2(Length + Breadth)
= 2 (22 + 20)
= 2(42)
= 84 m
∴ Perimeter of the rectangular plot is 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.

Solution –
Given that,
Perimeter of the a rectangular sheet = 100 cm
Length of the rectangular sheet = 35 cm
Perimeter of the rectangle = 2 (Length + Breadth)
100 = 2 (35 + Breadth)

= 35 + Breadth

50 – 35 = Breadth
Breadth = 15 cm
Then,
Area of the rectangle = Length × Breadth
= 35 m× 15 m
= 525 cm²
∴ Area of the rectangular sheet is 525 cm²

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.

Solution –
Given that,
Side of the square park = 60 m
Length of the rectangular park = 90 m
Area of the square park = (one of the side of square)²
= 60²
= 3,600 m²
Area of the rectangular park = 3600 m²
Length × Breadth = 3600
90 × Breadth = 3600
Breadth =

Breadth = 40 m
Hence, the required breadth = 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?

Solution –
Given that,
Length of the rectangle = 40 cm
Breadth of the square = 22 cm
Perimeter of the rectangle = Perimeter of the Square
2 (Length + Breadth) = 4 × side
2 (40 + 22) = 4 × side
2 (62) = 4 × side
124 = 4 × side
Side =

Side = 31 cm

So, Area of the rectangle = (Length × Breadth)
= 40 m × 22 m
= 880 cm²
Area of square = side²
= 31²
= 31 × 31
= 961 cm²

Since 961 cm² > 880 cm²
Hence, the square 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.

Solution –
Given that,
Perimeter of the rectangle = 130 cm
Breadth of the rectangle = 30
Perimeter of rectangle = 2 (Length + Breadth)
130 = 2 (length + 30)

= length + 30

Length + 30 = 65
Length = 65 – 30
Length = 35 cm

Then,
Area of the rectangle = Length × Breadth
= 35 m × 30 m
= 1050 cm²

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 (Fig). Find the cost of white washing the wall, if the rate of white washing the wall is ₹ 20 per m².

Solution –
Given that,
Length of the door = 2 m
Breadth of the door = 1 m
Length of the wall = 4.5 m
Breadth of the wall = 3.6 m
Area of the door = Length × Breadth
= 2 m × 1 m
= 2 m²

Area of the wall = Length × Breadth
= 4.5 × 3.6
= 16.2 m²

So, Area to be white washed = 16.2 m² – 2 m² = 14.2 m²
Cost of white washing 1 m² area = ₹ 20
Hence cost of whit washing 14.2 m² area = 14.2 × 20
= ₹ 284