Chapter – 11
Perimeter and area
Exercise – 11.1
Q1. The length and the breadth of a rectangular piece of land are 500m and 300m, respectively . Find
- Its area (ii) the cost of the land, if 1m2 of the land costs Rs 10000.
Solution:-
From the question it is given that,
Length of the rectangular piece of land = 500m
Breadth of the rectangular piece of land = 300m
Then,
- Area of rectangle = Length x Breadth
= 500 x 300
= 150000m2
- Cost of land for 150000m2 = 10000 x 150000
= Rs 1500000000
Q2. Find the area of square park whose perimeter is 320m.
Solution:-
From the question it is given that,
Perimeter of the square park = 320m
4 x Length of the side of park = 320m
Then,
Length of the side of park = 320/4
= 80m
So, Area of the square park = (Length of the side of park)2
= 802
= 6400m2.
Q3. Find the breadth of a rectangular plot of land , if its area is 440m2 and the length is 22m. Also find the perimeter .
Solution:-
From the question it is given that,
Area of rectangle = Length x Breadth
440 = 22 x breadth
Breadth = 440/22
Breadth = 20m
Then,
Perimeter of rectangle = 2(length + breadth)
= 2(22+20)
=2(42)
= 84m
Q4. The perimeter of a rectangular sheet is 100 cm . If the length is 35 cm, find its breadth.
Also find the area.
Solution:-
Perimeter of the rectangle = 2(length + breadth)
100 = 2(35 + Breadth)
(100/2) = 35 + Breadth
50 – 35 = Breadth
Breadth = 15 cm.
Area of rectangle = Length x Breadth
= 35 x 15
= 525 cm2
Q5. The area of a square park is the same as of a rectangular park. If side of the square park is 60m and the length of the rectangular park is 90m. find the breadth of the park .
Solution:-
Area of the square = (side)2
= (60)2
= 3600 m2
Area of rectangle = Length x Breadth
3600 = 90 x Breadth
3600/90 = Breadth
40 m = Breadth
Q6. A wire is in the shape of a rectangle. Its length is 40cm. And the breadth is 22 cm. If the same wire is rebent in the shape of a square , what will be thee measures of each side ?
Also find which shape encloses more area ?
Solution:-
Perimeter of rectangle = Perimeter of the square
2(40 + 22) = 4 x side
2(62) = 4 x side
124 = 4 x side
Side = 124/4
Side = 31 cm
Area of rectangle = 40 x 22
= 880 cm2
Area of square = (side)2
= (31)2
= 961 cm2
Q7. The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30cm, find its length Also find the area of rectangle .
Solution:-
Perimeter of rectangle = 2( Length + Breadth)
130 =2(Length + 30)
130/2 = Length + 30
Length + 30 = 65
Length = 65 – 30
Length = 35 cm.
Area of rectangle = Length x Breadth
= 35 x 30
= 1050 cm2
Q8. A door of length 2m and breadth 1m 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 per m2 .
Solution:-
Area of door = 2 x 1
= 2m2.
Area of wall = 4.5 x 3.6
= = 16.2 m2
So Area to be white washed = 16.2 – 2 = 14.2 m2
Cost of white washing 1m2 area = Rs 20
Hence cost of the white washing 14.2 m2 area = 14.2 x 20
= Rs 284