Perimeter and Area - Solutions

 CBSE Class –VII Mathematics

NCERT Solutions
Chapter 11 Perimeter and Area (Ex. 11.1)

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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$m^2$of the land costs Rs. 10,000.

Answer: 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$m^2$

(ii) Since, the cost of 1 m2$m^2$land = Rs. 10,000

Therefore, the cost of 1,50,000 m2 land = 10,000 x 1,50,000

= Rs. 1,50,00,00,000

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

Answer: Given: Perimeter of square park = 320 m

⇒$\Rightarrow$ 4 x side = 320

⇒$\Rightarrow$ side = 3204$\frac{320}{4}$ = 80 m

Now, Area of square park = side x side

= 80 x 80 = 6400 m2$m^2$

Thus, the area of square park is 6400 m2$m^2$.

Question 3. Find the breadth of a rectangular plot of land, if its area is 440 m2$m^2$ and the length is 22 m. Also find its perimeter.

Answer: Area of rectangular park = 440 m2$m^2$

⇒$\Rightarrow$ length x breadth = 440 m2$m^2$

⇒$\Rightarrow$ 22 x breadth = 440 ⇒$\Rightarrow$ breadth = 44022$\frac{440}{22}$ = 20 m

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

= 2 (22 + 20)

= 2 x 42 = 84 m

Thus, the perimeter of rectangular park 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: Perimeter of the rectangular sheet = 100 cm

⇒$\Rightarrow$ 2 (length + breadth) = 100 cm

⇒$\Rightarrow$ 2 (35 + breadth) = 100 ⇒$\Rightarrow$ 35 + breadth = 1002$\frac{100}{2}$

⇒$\Rightarrow$ 35 + breadth = 50 ⇒$\Rightarrow$ breadth = 50 – 35

⇒$\Rightarrow$ breadth = 15 cm

Now, Area of rectangular sheet = length x breadth

= 35 x 15 = 525 cm2$c{m}^2$

Thus, breadth and area of rectangular sheet are 15 cm and 525 cm2$c{m}^2$respectively.

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: Given: The side of the square park = 60 m

The length of the rectangular park = 90 m

According to the question,

Area of square park = Area of rectangular park

⇒$\Rightarrow$ side x side = length x breadth

⇒$\Rightarrow$ 60 x 60 = 90 x breadth

⇒$\Rightarrow$ breadth = 60×6090$\frac{60\times 60}{90}$ = 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: According to the question,

Perimeter of square = Perimeter of rectangle

⇒$\Rightarrow$ 4 x side = 2 (length + breadth)

⇒$\Rightarrow$ 4 x side = 2 (40 + 22) ⇒$\Rightarrow$ 4 x side = 2 x 62

⇒$\Rightarrow$ side = 2×624$\frac{2\times 62}{4}$ = 31 cm

Thus, the side of the square is 31 cm.

Now, Area of rectangle = length x breadth = 40 x 22 = 880 cm2$c{m}^2$

And Area of square = side x side = 31 x 31 = 961 cm2$c{m}^2$

Therefore, on comparing, the area of square is greater than that 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: Perimeter of rectangle = 130 cm

⇒$\Rightarrow$ 2 (length + breadth) = 130 cm

⇒$\Rightarrow$ 2 (length + 30) = 130 ⇒$\Rightarrow$ length + 30 = 1302$\frac{130}{2}$

⇒$\Rightarrow$ length + 30 = 65 ⇒$\Rightarrow$ length = 65 – 30 = 35 cm

Now area of rectangle = length x breadth = 35 x 30 = 1050 cm2$c{m}^2$

Thus, the area of rectangle is 1050 cm2$c{m}^2$.

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 Rs. 20 perm2$m^2$.

Answer: Area of rectangular door = length x breadth = 2 m x 1 m = 2 m2$m^2$

Area of wall including door = length x breadth = 4.5 m x 3.6 m = 16.2 m2$m^2$

Now, Area of wall excluding door

= Area of wall including door – Area of door

= 16.2 – 2 = 14.2m2$m^2$

Since, The rate of white washing of 1 m2$m^2$the wall = Rs. 20

Therefore, the rate of white washing of 14.2m2$m^2$ the wall = 20 x 14.2

= Rs. 284

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