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.

Answer:

(i) Length of the rectangular piece

(1) = 500 m

Breadth of the rectangular piece

(b) = 300 m

Area = 1 × b sq. unit

= 500 × 300 m^{2}

= 150000m^{2}

(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.

Answer:

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 m^{2}

= 6400 m^{2}

Question 3.

Find the breadth of a rectangular plot of land, if its area is 440 m^{2} and the length is 22 m. Also find its perimeter.

Answer:

Length of the rectangular plot = 22 m

Area of the rectangular plot = 440 m^{2}

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 cm^{2}

= 525 cm^{2}

Thus,

(i) Breadth of the rectangular sheet = 15 cm

(ii) Area of the rectangular sheet = 525 cm^{2}

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.

Answer:

Side of the square park = 60 m

Area of the square park = 60 × 60 m^{2}

= 3600 m^{2}

Length of the rectangular park = 90 m

Area of the rectangular Park

= Area of the square park = 3600 m^{2}

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?

Answer:

Length of the wire

(l) = 40 cm

Breadth of the wire

(b) = 22 cm

Area of the rectangle = 1 × b

= 40 × 22 cm^{2}

= 880 cm^{2}

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 cm^{2}

= 961 cm^{2}

961 cm^{2} > 880 cm^{2}

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.

Answer:

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 cm^{2}

= 1050 cm^{2}

∴ 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 m^{2}.

Answer:

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 m^{2}

= \(\frac{45}{10} \times \frac{36}{10}\) m^{2}

= \(\frac{1620}{100}\) m^{2}

= 16.2 m^{2}

Area of the door = 2 m × 1 m

(l = 2 m, b = 1 m) = 2 m^{2}

Area to be white washed =

Area of the wall – Area of the door

= 16.2 m^{2} – 2 m^{2}

= 14.2 m^{2}

Rate of white washing per m^{2} = ₹ 20

∴ Cost of while washing = ₹ 20 × 14.2

= ₹ 284