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

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Perimeter and Area Class 7 Ex 11.2
    Perimeter and Area Class 7 Ex 11.3
    Perimeter and Area Class 7 Ex 11.4
    Perimeter and Area Class 7 MCQ

(Chapter – 11) (Perimeter and Area) 

(Class – VII)

 

Exercise 11.1

Question 1: 

The length and 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 1: 

Given: Length of a rectangular piece of land = 500 m and

Breadth of a rectangular piece of land = 300 m

(i) Area of a rectangular piece of land = Length x Breadth 

= 500 x 300 

= 1,50,000 m²

(ii) Since, the cost of 1 m² land = ₹10,000

Hence, the cost of 1,50,000 m² land = ₹(10,000 x 1,50,000) 

 = ₹1,50,00,00,000

Question 2: 

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

Answer 2: 

Given: Perimeter of square park = 320 m

4 x side = 320 [perimeter of a square = 4×side]

side of the square= (320 / 4) m

= 80 m

Now, Area of square park = side x side = 80 x 80 = 6400 m²

Thus, the area of square park is 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.

Answer 3: 

Area of the rectangular plot = 440 m²

length x breadth = 440 m²  [area of the rectangle = length × breadth]

→22 x breadth = 440

→breadth =( 440 / 22) 

= 20 m

Now, Perimeter of rectangular plot = 2 (length + breadth)

= 2 (22 + 20)

= 2 x 42 = 84 m

Thus, the perimeter of the rectangular plot of land 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.

Answer 4: 

Perimeter of the rectangular sheet = 100 cm

→2 (length + breadth) = 100 cm [perimeter of rectangle = 2(length × breadth) 

→2 (35 + breadth) = 100

→35 + breadth =( 100\2 ) 

→35 + breadth = 50

→breadth = 50 – 35

→breadth = 15 cm

We know, Area of rectangular sheet = length x breadth

= 35 x 15 = 525 cm²

Thus, the breadth of the rectangular sheet is 15 cm and area of the rectangular sheet is 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 cm, find the breadth of the rectangular park.

Answer 5: 

Given: The side of the square park = 60 m

Therefore area of the square Park = (side × side ) = 60 × 60 = 360 m²

The length of the rectangular park = 90 m

According to the question,

Area of rectangular park = Area of square park

→ length x breadth = 360

→ 90 x breadth = 360

breadth = ( 360 / 90 ) 

= 40 m

Thus, the breadth of the rectangular park is 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 6: 

Given length of the rectangle = 40 cm

 and breadth of the rectangle = 22 cm

Since same length of wire rebent to form one time a rectangle and another time a square

Therefore, Perimeter of square = Perimeter of rectangle 

→4 x side = 2 (length + breadth)

→4 x side = 2 (40 + 22)

→4 x side = 2 x 62

→side = (2 × 62 ) / 4

= 31 cm

Thus, the side of the square is 31 cm.

Now, Area of rectangle = length x breadth = 40 x 22 = 880 cm²

And Area of square = side x side = 31 x 31 = 961 cm²

Therefore, by comparing, the area of the square is greater than that of the 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 7: 

Given, perimeter of the rectangle = 130 cm and breadth of the rectangle = 30 cm

Now, Perimeter of rectangle = 130 cm

→2 (length + breadth) = 130 cm

→2 (length + 30) = 130

→length + 30 = (130 / 2 ) 

→length + 30 = 65

→length = 65 – 30 = 35 cm

Now area of the rectangle = length x breadth = 35 x 30 = 1050 cm²

Thus, the area of the rectangle is 1050 cm².

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.

Answer 8: 

Area of rectangular door = length x breadth = 2 m x 1 m = 2 m²

Now, area of wall including door = length x breadth = 4.5 m x 3.6 m = 16.2 m²

Now, Area of wall excluding door

= Area of wall including door – Area of door

= 16.2 – 2 = 14.2 m²

Since cost of white washing of the wall is ₹20 per square metre,

Therefore, the total cost of white washing of 14.2 m² the wall = (20 x 14.2) 

= ₹284

Thus, the cost of white washing the wall excluding the door is ₹284.