Mathematics - Class 7 - Chapter 11 - Perimeter and Area - 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:

(i) Its area

Given,

Length of the rectangular piece of land = 500 m

Breadth of the rectangular piece of land = 300 m

Now,

Area of rectangle = Length × Breadth

= 500 × 300

= 150000 m²

(ii) the cost of the land, if 1 m² of the land costs ₹ 10,000.

Cost of the land for 1 m² = ₹ 10000

Cost of the land for 150000 m² = 10000 × 150000

= ₹ 1500000000

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

Solution:

Given,

The perimeter of the square park = 320 m

Then,

4 × Length of the side of the park = 320 m

Now,

Length of the side of the park = 320/4

= 80 m

Hence, the Area of the square park = (length of the side of the park)²

= 80²

= 6400 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,

Area of the rectangular plot = 440 m²

Length of the rectangular plot = 22 m

We know,

Area of the rectangle = Length × Breadth

440 = 22 × Breadth

Breadth = 440/22

Breadth = 20 m

Now,

Perimeter of the rectangle = 2(Length + Breadth)

= 2 (22 + 20)

= 2(42)

= 84 m

Hence, 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,

Perimeter of the rectangular sheet = 100 cm

Length of the rectangular sheet = 35 cm

We know,

Perimeter of the rectangle = 2 (Length + Breadth)

100 = 2 (35 + Breadth)

(100/2) = 35 + Breadth

50 – 35 = Breadth

Breadth = 15 cm

Now,

Area of the rectangle = Length × Breadth

= 35 × 15

= 525 cm²

Hence, 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,

Area of a square park is the same as of a rectangular park.

Side of the square park = 60 m

Length of the rectangular park = 90 m

We know,

Area of the square park = (side)²

= 60²

= 3600 m²

Given, Area of the rectangular park = 3600 m²

Length × Breadth = 3600

90 × Breadth = 3600

Breadth = 3600/90 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:

According to the question, we can conclude that the perimeter of the square is the same as the perimeter of the rectangle.

Given,

Length of the rectangle = 40 cm

Breadth of the square = 22 cm

So,

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 = 124/4

Side = 31 cm

Now, Area of the rectangle = (Length × Breadth)

= 40 × 22

= 880 cm²

Area of square = side²

= 31²

= 961 cm²

Hence, Square shaped wire 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,

Perimeter of the rectangle = 130 cm

Breadth of the rectangle = 30

We know,

Perimeter of rectangle = 2 (Length + Breadth)

130 = 2 (length + 30)

130/2 = length + 30

Length + 30 = 65

Length = 65 – 30

Length = 35 cm

Now,

Area of the rectangle = Length × Breadth

= 35 × 30

= 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.