HBSE 7th Class Maths Solutions Chapter 11 Perimeter and Area Ex 11.1

Haryana State Board HBSE 7th Class Maths Solutions Chapter 11 Perimeter and Area Ex 11.1 Textbook Exercise Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 11 Perimeter and Area  Exercise 11.1

Question 1.
The length and breadth of a rectangular piece of land is 500 m and 300 m respectively. Find:
(i) its area
(ii) the cost of the land ofl m2 is Rs. 10000.
Solution:
(i) The area of rectangular piece of land = l x b = 500 m x 300 m = 150000 m².
(ii) The cost of 1 m² of the land = Rs. 10000
∴ the cost of 150000 m²
= Rs. 10000 x 150000 m² = Rs. 1,50,00,00,000.

Question 2.
Find the area of a square park whose perimeter is 320 m.
Solution:
Perimeter of square = 4 x side
320 m = 4 x side
or, 4 x side = 320 m
or side = \(\frac{320}{4}\)m = 80 m.
So, area of square = side x side
= 80 m x 80 m = 6400 m².

Question 3.
Find the breadth of the rectangular plot of land, if its area is 440 m². and the length is 22 m. Also find its perimeter.
Solution:
The area of rectangular plot = 440 sq. m.
Length = 22 m
Breadth = ?
So, the area of rectangular plot = l x b
440 sq. m. = 22 m x breadth (b)
or, 22 m x breadth = 44 sq. m
or b = \(\frac{440 \mathrm{~m}^{2}}{22 \mathrm{~m}}\) = 20 m.
Perimeter of rectangular plot of land = 2 (l+b)
= 2 x (22 m + 20 m)
= 2 x 42 = 84 m

Question 4.
The perimeter of rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find its area.
Solution:
Perimeter of rectangular sheet = 100 cm
Length = 35 cm
Breadth = ?
Area of rectangular sheet = ?
∴ Perimeter of rectangular sheet = 2 x (l + b)
100 m = 2(35 + 6)
or, 100 cm = 70 + 2b
or, 100 – 70 = 2b
or, 30 = 2b
or, b = \(\frac{30}{2}\) = 15
∴ breath = 15 cm
And, Area = l x 6 = 35 x 15
∴ Area = 525 cm2.

Question 5.
The area of 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:
The area of the square park
= side x side = 60 m x 60 m = 3600 m².
So, according to question,
Area of square park
= area of rectangular park
∴ 3600 m²
= area of rectangular park
Now, Area of rectangular park = l x b
3600 m²
= 90 x b
or, b = \(\frac{3600 \mathrm{~m}^{2}}{90 \mathrm{~m}}\) = 40 cm
Hence the breadth of the rectangular park = 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 enclose more area.
Solution:
length of rectangle = 40 cm
breadth of rectangle = 22 cm
Since, perimeter of rectangle = perimeter of square
Hence 2(1 + 6) = 4 x side
or, 4 x side = 2(1 + 6)
∴ side = \(\frac{2(1+\mathrm{b})}{4}=\frac{2 \times(40 \mathrm{~cm}+22 \mathrm{~cm})}{4}=\frac{2 \times 62 \mathrm{~cm}}{4}\)
Side of square =31 cm.
Now, Area of rectangle = l x b
= 40 cm x 22 cm = 880 cm².
Area of square = side x side = 31 cm x 31 cm
= 961 cm².
Hence, square encloses more area.

Question 7.
The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30cm, find its length. Also find the area of the rectangle.
Solution:
Perimeter of rectangle = 130 cm
Length = ?
Breadth = 30 cm
Area of rectangle = ?
Now,Perimeter of rectangle = 2(l + b)
130 = 2(l + 30)
or, 130 = 2l + 60
or, 130 – 60 = 2l
or, 70 = 2l
or, l = \(\frac{70}{2}\) = 35 cm.
∴ Length = 35 cm
And, Area of rectangle = l x b
= 35 x 30
= 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 of the wall is Rs. 20 per m².

Solution:
Area of a door = l x b
= 1 m x 0.5 = 0.5 m².
Area of the wall = l x b
= 4.5m x 3.6m=16.20m².
∴ Area of the = 16.20 – 0.5 = 15.70 m².
rest of the wall
Now, ∵ The rate of white washing of the 1 m² wall = 20 Rs.
∴ The rate of white washing of the 15.70 m2 wall = 15.70 x 20 = Rs. 314.