Solution of NCERT Exercise 11.1
Perimeter and Area 7th Math
Solution of NCERT 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 1m2 of the land costs Rs 10,000.
Solution:
(i) Its area
Given,
Length of the rectangular park = 500 m
Breadth of the rectangular park = 300 m
∴ Area of rectangular park = ?
We know that,
Area of a rectangle = Length × Breadth
∴ Area of given rectangular park = 500 m × 300 m
∴ Area of rectangular park = 150000 m2 Answer.
(ii) The cost of the land, if 1 m2 of the land costs Rs. 10,000.
∵ Cost of 1 m2 of land = Rs 10, 000.
∴ Cost of 150000 m2 of land = Rs 10,000 × 150000
= Rs 1500000000.00
∴ Cost of land = Rs 1500000000.00 Answer.
Question (2) Find the area of a square park whose perimeter is 320 m.
Solution:
Given,
Perimetre of square park = 320 m
∴ Area of that square park = ?
Let side of given square park = a
We know that;
Perimetre of a square = 4 × side.
⇒ 320 m = 4 × a
⇒ 4 × a = 320 m
⇒ a = `320/4` m = 80 m
Thus side of give square park = 80 m
Now we know that,
Area of a square = side2
∴ Area of given square park = (80 m)2
= 80 m × 80 m
= 6400 m2
∴ Area of given square park = 6400 m2 Answer.
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.
Solution:
Given,
Area of the rectangular park = 440 m2
And, Length of that rectangular park = 22 m
∴ Breadth of the rectangular park = ?
Let Breadth of given rectangular park = b
We know that,
Area of a rectangle = Length × Breadth
⇒ 440 m2 = 22m × b
⇒ 22 m × b = 440 m2
`=> b = (440 m^2)/(22 m)`
⇒ b = 20 m
We know, that
Perimeter of rectangle = 2(Length + Breadth)
Thus, perimeter of given rectangular plot = 2(22 m + 20 m)
=2 × 42 m
= 84 m
Thus, perimeter of given rectangular plot = 84 m
∴ Breadth of the given rectangular park = 20 m and Perimeter = 84 m Answer.
Question (4) The perimetre of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.
Solution:
Given,
Perimetre of the rectangular sheet = 100 cm
And, Length of that sheet = 35 cm
∴ Breadth and area of that sheet = ?
Let breadth of the given rectangular sheet = b
We know that,
Perimetre of a rectangle = 2 ( Length + Breadth)
⇒ 100 cm = 2(35 cm + b)
⇒ 100 cm = 70 cm + 2p
⇒ 70 cm + 2b = 100 cm
⇒ 2b = 100 cm – 70 cm
⇒ 2b = 30 cm
⇒ b = `30/2` cm = 15 cm
∴ Breadth of given sheet = 15 cm
Now, we know that,
Area of rectangle = Length × Breadth
∴ Area of given rectangular sheet = 35 cm × 15 cm
= 525 cm2
Therefore, Breadth of given sheet = 15 cm; and area of that rectangular sheet = 525 cm2 Answer.
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.
Solution:
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.
∴ Breadth of rectangular park = ?
We know that,
Area of a square = Side2
∴ Area of given square park = (60 m)2
= 60 m × 60 m
= 3600 m2
Let Breadth of the given rectangle park = b
Now, we know that,
Area of a rectangle = Length × Breadth
∴ Area of given rectangular park = 90 m × b
⇒ 3600 m2 = 90 m × b
[∵ As per question, area of rectangular park = area of square park = 3600 m2 (As calculated above)]
⇒ 90 m × b = 3600 m2
`:. b = (3600 m^2)/(90 m)=40m`
∴ Breadth of given rectangular park = 40 m Answer.
Question (6) A wire is in the shape of 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 its side? Also find which shape encloses more area?
Solution:
Given,
Length of the rectangle = 40 cm.
And, Breadth = 22 cm.
Then the side of the square made after rebent of same wire from which rectangle was made = ?
We know that,
Perimetre of rectangle = 2 (Length + Breadth)
= 2(40 cm + 22 cm)
= 2 × 62 cm
= 124 cm
∴ Perimetre of the rectangle = 124 cm.
Since, square is made after rebending of same wire
∴ Perimetre of square = Perimetre of the rectangle.
Now, we know that,
Perimetre of a square = 4 × side.
⇒ 124 cm = 4 × side
[ ∵ Perimetre of the square = Perimetre of the rectangle = 124 cm]
⇒ 4 × side = 124 cm
⇒ side = `124/4` cm = 31 cm
Thus, side of square = 31 cm.
Now, Area of square = side2
∴ Area of given square = (31 cm )2
= 31 cm × 31 cm
= 961 cm2
And, we know that,
Area of Rectangle = Length × Breadth
Thus, area of given rectangle = 40 cm &# 215; 22 cm
= 880 cm 2
Therefore,
Side of square = 31 cm. And square will enclose more area. Answer
Question (7) The perimetre 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.
Solution:
Given,
Perimetre of Rectangle = 130 cm
Breadth of rectangle = 30 cm
Length = ?
And area = ?
Let Length of the rectangle = m
We know that ,
Perimetre of a rectangle = 2 (Length + Breadth)
⇒ 130 cm = 2(m + 30 cm)
⇒ 130 cm = 2m + 60 cm.
⇒ 2m + 60 cm = 130 cm
⇒ 2 m = 130 – 60 cm
⇒ 2 m = 70 cm
⇒ m = `70/2 `=35 cm.
∴ Legth of therectangle= 35 cm.
Now we know that area of rectangle = Length × Breadth
Thus area of given rectangle = 35 cm × 30 cm
= 1050 cm2
Thus, length f the rectangle = 35 cm; and area of the rectangle =1050 cm2 Answer
Question (8) 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 (figure). Find the cost of white washing the wall, if the rate of white washing the wall is Rs 20 per m2.
Solution:
Given,
Length of wall = 4.5 m
Breadth of wall = 3.6 m
Length of door = 2m
Breadth of door = 1 m
Rate of white washing = Rs 20 per m2
∴ Total cost of white washing of wall =?
We know that,
Area of a rectangle = Length × Breadth
∴ Area of wall = 4.5 m × 3.6 m
= 16.20 m2
Now, Area of the door = length × breadth
= 2m × 1m
=2 m2
Now surface area of wall excluding the door
= Area of wall including the door – Area of door
= 16.2 m2 – 2 m2
= 14.2 m2
Thus Area of wall excluding door = 14.2 m2
Now,
∵ Cost of white washing of 1 m2 = Rs 20.00
∴ Cost of white washing of 14.2 m2
= Rs 20.00 × 14.2
= Rs 284.00
∴ Cost of white washing of wall = Rs 284.00 Answer
Reference: