## 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: **

Given

Length of rectangular land = 500 m

Breadth of rectangular land = 300 m

To find = Area

Cost of land

**(i)**Area of rectangle = l x b

= 500 x 300

= 150000 m²

Therefore, the area of the rectangular land is 150000 m².

**(ii)**Area of rectangular land = 150000 m²

Cost of 1 m² land = ₹ 10000

Cost of 150000 m² land = ?

= 10000 x 150000

= ₹ 1,50,00,00,000

Therefore, the cost of the land is ₹ 1,50,00,00,000.

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

Answer:

Given

Answer:

Perimeter of a square park = 320 m

To find - Side length

Area

Side = perimeter/4

= 320/4

= 80 m

Therefore, the length of each side is 80 m.

Area of Square = side x side

= 80 x 80

= 6400 m²

Therefore, 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:

Given

Answer:

Area of rectangular plot = 440 m²

Length of rectangular plot = 22 m

To find - Breadth

Perimeter

Breadth = Area/Length

= 440/22

= 20 m

Therefore, the breadth of the rectangular plot is 20 m.

Perimeter of a rectangle = 2 x (l + b)

= 2 x (22 + 20)

= 2 x 42

= 84 m

Therefore, the 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.**

Answer:

Given

Answer:

Perimeter of rectangular sheet = 100 cm

Length of rectangular sheet = 35 cm

To find = Breadth

Area

Perimeter of rectangle = 2 x (l + b)

100 = 2 x (35 + b)

100 = (2 x 35) + (2 x b)

100 = 70 + 2b

2b = 100 - 70 = 30

2b = 30

b = 30/2

b = 15 m

Therefore, the breadth of the rectangular sheet is 15 m.

Area of rectangle = l x b

= 35 x 15

= 525 m²

Therefore, the area of rectangular sheet is 525 m².

**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:

Answer:

Given

Area of Square park = Area of rectangular park

Length of side of square park = 60 m

Length of rectangular park = 90 m

To find = Area

Breadth

Area of square = side x side

= 60 x 60

= 3600 m²

Breadth of rectangle = area/length

= 3600/90

= 40 m

Therefore, the breadth of 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:

Given

Answer:

Length of rectangle = 40 cm

Breadth of rectangle = 22 cm

To find = Perimeter

Side of square

Which shape encloses more area

Perimeter of rectangle = 2 x (l + b)

= 2 x (40 + 22)

= 2 x 62

= 124 cm

Therefore, the perimeter of rectangle is 124 cm.

Perimeter of Square = Perimeter of Rectangle

Length of side of square = perimeter/4

= 124/4

= 31 cm

Therefore, the length of side of square is 31 cm.

Area of rectangle = length x breadth

= 40 x 22

= 880 cm²

Area of square = side x side

= 31 x 31

= 961 cm²

Compare

880 cm² < 961 m²

Therefore, square encloses more area.

**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:

Given

Answer:

Perimeter of rectangle = 130 m

Breadth = 30 cm

To find = Length

= Area

Perimeter of rectangle = 2 x (l + b)

130 = 2 x (l + 30)

130 = (2 x l) + (2 x 30)

2l = 130 - 60

2l = 70

l = 70/2

l = 35

Therefore, length of a rectangle is 35 cm.

Area of rectangle = l x b

= 35 x 30

= 1050 cm²

Therefore, the area of 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 m

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:

Answer:

Given

Length of wall = 4.5 m

Breadth of wall = 3.6 m

Door length = 2 m

Door breadth = 1 m

Rate of white washing = ₹ 20 per m²

To find = Area to be white washed

= Cost of white washing

Area of rectangle = l x b

= 4.5 x 3.6

= 16.2 m²

Therefore, the area of wall = 16.2 m².

Area of rectangle = l x b

= 2 x 1

= 2 m²

Therefore, the area of door is 2 m².

Area to be white washed = area of wall - area of door

= 16.2 m² - 2 m²

= 14.2 m²

Therefore, the area to be white washed is 14.2 m².

Cost of white washing 1 m² = ₹ 20

Cost of white washing 14.2 m² = ?

= 20 x 14.2

= ₹ 284

Therefore, the cost of white washing the wall is ₹ 284.

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