NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.1

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.1 are the part of NCERT Solutions for Class 8 Maths. Here you can find the NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.1.

Ex 11.1 Class 8 Maths Question 1.

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Solution:
Perimeter of the figure (a) = 4 × side = 4 × 60 = 240 m
Perimeter of the figure (b) = 2[l + b] = 2[80 + b] m
Perimeter of the figure (a) = Perimeter of the figure (b)
⇒ 240 = 2[80 + b]
⇒ 80 + b = 120
⇒ b = 120 – 80 = 40 m
Area of the figure (a) = (side)² = 60 × 60 = 3600 m²
Area of the figure (b) = l × b = 80 × 40 = 3200 m²
So, the area of the figure (a) is larger than the area of the figure (b).

Ex 11.1 Class 8 Maths Question 2.

Mrs Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of ₹ 55 per m².

Solution:
Area of the plot = side × side = 25 m × 25 m = 625 m²
Area of the house = l × b = 20 m × 15 m = 300 m²
Area of the garden to be developed = Area of the plot – Area of the house

= 625 m² – 300 m² = 325 m²
The total cost of developing the garden = ₹ 325 × 55 = ₹ 17,875

Ex 11.1 Class 8 Maths Question 3.

The shape of a garden is rectangular in the middle and semicircular at the ends as shown in the diagram. Find the area and the perimeter of this garden. [Length of rectangle is 20 – (3.5 + 3.5) metres]

Solution:
Length of the rectangle = 20 – (3.5 + 3.5) = 20 – 7 = 13 m
Area of the rectangle = l × b = 13 × 7 = 91 m²
Area of two circular ends = 2(1/2 πr²)
= πr²
= 22/7 × 7/2 × 7/2
= 77/2 m²
= 38.5 m²
Total area of the garden = Area of the rectangle + Area of two ends

= 91 m² + 38.5 m² = 129.5 m²
Total perimeter of the garden = 13 + 13 + 2 × (πr)
= 26 + 2(22/7 × 7/2)
= 26 + 22
= 48 m

Ex 11.1 Class 8 Maths Question 4.

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 m²? (If required you can split the tiles in whatever way you want to fill up the corners).

Solution:
Area of the floor = 1080 m² = 1080 × 10000 cm² = 10800000 cm²

[∵ 1 m² = 10000 cm²]
Area of 1 tile = base × height = 24 × 10 = 240 cm²
Number of tiles required

= 45000 tiles

Ex 11.1 Class 8 Maths Question 5.

An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, the circumference of a circle can be obtained by using the expression C = 2πr, where r is the radius of the circle.