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.
Given: length of the rectangular land = 500 m
Breadth of the rectangular land = 300 m
Rate of the land = 10000
Area of the land = length X breadth
= 500 X 300
= 150000 m2
The cost of the land = Rate X Area
= 10000 X 150000
= ₹ 1500000000
Ans: area of the land = 150000 m2
Cost of the land = ₹ 1500000000
2). Find the area of a square park whose perimeter is 320 m.
Given: Perimeter of the square = 320 m
Perimeter of the square = 4 X side
4 X side = 320
Length = (320)÷ 8
= 40 m
Area of the square = side X side
= 40 X 40
= 1600 m2
Ans: area of the square = 1600 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.
Given: length of the rectangular plot = 22 m
Area of the plot = 440 m2
To Find: breadth of the rectangular plot = ?
Perimeter = ?
Area of the plot = length X breadth
440 = 22 X breadth
22 X breadth = 440
breadth = 440 ÷ 22
breadth = 20
perimeter = 2 (length + breadth)
= 2 (22 + 20)
= 2 X 42
= 84 m.
Ans: breadth of the rectangular plot = 20 m
Perimeter of the rectangular plot = 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.
Given: perimeter of rectangular sheet = 100 cm
Length of the sheet = 35 cm
To find: breadth of the sheet = ?
Area of the sheet = ?
Perimeter of the sheet = 100
2(length + breadth) = 100
2(35 + breadth) = 100
35 + breadth = 100 ÷ 2
35 + breadth = 50
Breadth = 50 – 35
breadth = 15 cm
area of the sheet = length X breadth
= 35 X 15
= 525 sq cm.
Ans: breadth of the sheet = 15 cm
Area of the sheet = 525 sq cm
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.
Given: side of the square park = 60 m
Length of the rectangular park = 90 m
Area of the square park = area of the rectangular park
To find: breadth of the rectangular park = ?
Area of the square park = area of the rectangular park
Side2 = length X breadth
602 = 90 X breadth
90 X breadth = 602
breadth = 3600 ÷ 90
breadth = 40
Ans: breadth to the rectangular park = 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?
Given: length of the rectangle = 40 cm
breadth of the rectangle = 22 cm
perimeter of rectangle = perimeter of the square
To find: side of the square = ?
Which shape has more area
Perimeter of the square = perimeter of the rectangle
4 X side = 2(length + breadth)
4 X side = 2(40+22)
4 X side = 2 X 62
4 X side = 124
Side = 124 ÷ 4
side = 31 cm
area of square = sideX side
= 31 X 31
= 961 sq cm
area of the rectangle = length X breadth
= 40 X 22
= 880 sq cm
Area of the square > area of the rectangle
Ans: side of the square = 31 cm
square shape 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.
Given: perimeter of a rectangle = 130 cm
breadth of the rectangle = 30 cm
To find: length of the rectangle = ?
area of the rectangle = ?
perimeter of rectangle = 130
2(length + breadth) = 130
2(length + 30)= 130
length + 30 = 130 ÷ 2
length = 65 – 30
length = 35 cm
area of the rectangle = length X breadth
= 35 X 30
= 1050 sq cm
Ans: length of the rectangle = 35 cm
area of the rectangle = 1050 sq cm
8). A door of length 2 m and breadth 1m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m (Fig11.6). Find the cost of white washing the wall, if the rate of white washing the wall is ₹ 20 per m2.
Given: length of the wall = L = 4.5 m
breadth of the wall = B = 3.6 m
length of the door = l = 2 m
breadth of the door = b = 1 m
rate of whitewashing the wall = ₹ 20 per m2
to find: cost of whitewashing the wall = ?
area of white washing the wall = area of the wall – area of the door
area of the wall = length X breadth
= 4.5 X 3.6
= 16.2 m2
area of the door = length X breadth
= 2 X 1
= 2 m2
area of white washing the wall = area of the wall – area of the door
= 16.2 – 2
= 14.2 m2
Cost of white washing = Rate X area
= 20 X 14.2
= ₹ 284
Ans: Cost of whitewashing the wall = ₹ 284
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