Chapter 11 Perimeter and Area Ex 11.1 Solutions
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 тВ╣ 10,000
Answer - 1 : -
Given: l = 500 m, b = 300 m
(i) Area = l ├Ч b
= 500 m ├Ч 300 m = 150000 m2
(ii) Cost of land = тВ╣ 10,000 ├Ч 150000 = тВ╣ 15,00,000,000
Question - 2 : - Find the area of a square park whose perimeter is 320 m.
Answer - 2 : -
Given:Perimeter = 320 m
Side of the square =┬а┬аPerimeter/┬а=320/4m=80m
Area of the square = Side ├Ч Side
= 80 m ├Ч 80 m = 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 : -
Given:Area = 440 m2
Length = 22 m
Breadth =┬а┬аArea/┬аLength┬а=440m2/22m=20m
Perimeter = 2[l + b] = 2 [22 m + 20 m]
= 2 ├Ч 42 m = 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 : -
Given: Perimeter = 100 cm
Length = 35 cm
Perimeter = 2(l + b)
100 = 2(35 + b)
100/2=35+b
тЗТ 50 = 35 + b
тЗТ b = 50 тАУ 35 = 15 cm
тИ┤ Breadth = 15 cm
Area = l ├Ч b = 35 cm ├Ч 15 cm
= 525 cm2
Question - 5 : - The area of a square park is 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 - 5 : -
Given:Side of the square park = 60 m Length of the rectangular park = 90 m Area ofthe rectangular park = Area of the square park
90 m ├Ч 6 = 60 m ├Ч 60 m
тЗТ┬аb=(60m├Ч60m)/90
тЗТ b = 40m
Hence, the required breadth = 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 = 40 cm, Breadth = 22 cm Perimeter of the rectangle
= Length of the wire
= 2(l + b) = 2(40 cm + 22 cm)
= 2 ├Ч 62 cm = 124 cm
Now, the wire is rebent into a square.
Perimeter = 124 cm
тЗТ 4 ├Чside = 124
тИ┤ side =┬а124┬аcm= 31 cm
So, the measure of each side = 31 cm
Area of rectangular shape = l ├Ч b
= 40 cm x 22 cm
= 880 cm2
Area of square shape = (Side)2
= (31)2┬а= 961 cm2
Since 961 cm2┬а> 880 cm2
Hence, the 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 - 7 : -
Given:Perimeter = 130 cm
Breadth = 30 cm
Perimeter = 2 (l + b)
130 cm = 2(l + 30 cm)
тЗТ┬а130┬аcm= l + 30 cm
тЗТ 65 cm= l + 30 cm
тЗТ 65 cmтАУ 30 cm = l
тИ┤ l = 35cm
Area of the rectangle = l ├Ч b = 35 cm ├Ч 30 cm
= 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 тВ╣ 20 per m2.
Answer - 8 : -
Given: Length of wall = 4.5 m
Breadth of the wall = 3.6 m
Length of the door = 2 m
Breadth of the door = 1 m
Area of the wall = l ├Ч b = 4.5 m ├Ч 3.6 m = 16.20 m2
= 16.20 m2
Area of the door = l ├Ч b = 2 m ├Ч 1 m = 2 m2
тИ┤ Areaof the wall to be white washed = Area of the wall тАУ Area of the door
= 16.20 m2┬атАУ 2 m2= 14.20 m2
Cost of white washing
= тВ╣ 14.20 ├Ч 20 = тВ╣ 284.00
Hence, the required area = 14.20 m2┬аandthe required cost = тВ╣ 284