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.

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