Class VII, NCERT (CBSE) Mathematics | Perimeter and Area (Chapter 11.1)

Class VII, NCERT (CBSE) Mathematics Text Book Exercise 11.1 Solution

(Page 208 - 209)

Q1: 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 Rs 10,000.

Ans:

(i) Area = (length × breadth)

= 500 × 300

= 150000 m²

(ii)Cost of 1 m² land = Rs 10000

Cost of 150000 m² land = 10000 × 150000 = Rs 1500000000

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

Ans:

Perimeter = 320 m

or, 4 × Length of the side of park = 320

or, Length of the side of park =

or, Area = (Length of the side of park)²

             = (80)² = 6400 m².

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

Ans:

Area = Length × Breadth = 440 m²

22 × Breadth = 440

or, Breadth = = 20 m

Perimeter = 2 (Length + Breadth)

                = 2 (22 + 20) = 2 (42) = 84 m²

Q 4: The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.

Ans:

Perimeter = 2 (Length + Breadth) = 100 cm

2 (35 + Breadth) = 100

35 + B = 50

B = 50 − 35 = 15 cm

Area = Length × Breadth = 35 × 15 = 525 cm²

Q 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.

Ans:

Area of square park = (One of its sides)² = (60)² = 3600 m²

Area of rectangular park = Area of square park (given)

or, Length × Breadth = 3600

or, 90 × Breadth = 3600

or, Breadth = 40 m.

Q 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?

Ans:

Perimeter of rectangle = Perimeter of square (given).

So, 2 (Length + Breadth) = 4 × Side

or, 2 (40 + 22) = 4 × Side

or, 2 × 62 = 4 × Side

or, Side = = 31 cm

Area of rectangle = 40 × 22 = 880 cm²

Area of square = (Side)² = 31 × 31 = 961 cm²

Therefore, the square-shaped wire encloses more area.

Q 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.

Ans:

Perimeter = 2 (Length + Breadth) = 130

or, 2 (Length + 30) = 130

or, Length + 30 = 65

or, Length = 65 − 30 = 35 cm

or, Area = Length × Breadth = 35 × 30 = 1050 cm².

Q 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 (see the given figure). Find the cost of white washing the wall, if the rate of white washing the wall is Rs 20 per m².

Ans:

Area of wall = 4.5 × 3.6 = 16.2 m²

Area of door = 2 × 1 = 2 m²

Area to be white-washed = 16.2 − 2 = 14.2 m²

Cost of white-washing 1 m² area = Rs 20

Hence, the cost of white washing the wall of 14.2 m² area

= 14.2 × 20 = Rs 284.