Class 8, CBSE Math Guide | Solutions of NCERT Mathematics Exercise 11.1 Mensuration

CBSE Board, Class VIII Mathematics

Chapter 11 Mensuration

Ncert Solutions of Mathematics Textbook Exercise 11.1 (Page 171)

Q.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:

(a) Perimeter of square = 4 (Side of the square) = 4 x 60 = 240 m

(b) Perimeter of rectangle = 2 (Length + Breadth) = 2 (80 + Breadth)

     or, 240 = 2 (80 + Breadth)

     or, 120 = 80 + Breadth

     or, Breadth = 40 m

Area of square = (Side)² = (60 m)² = 3600 m²

Area of rectangle = Length × Breadth = 80 m × 40 m = 3200 m²

Hence, square field has larger area than the area of the rectangular field.

Q.2: Mrs. Kaushik has a square plot with the measurement as shown in the following 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 Rs 55 per m².

Solution:

Area of garden = Area of square plot – Area of rectangular plot (middle plot)

                       = (25)² – (20 x 15) = 325 m²

The total cost of developing garden around the house at the rate of Rs 55 per m² = 55 × 325 = Rs 17,875

Q. 3: The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of the garden.

Solution:

Length of the rectangle = 20 – (3.5 + 3.5) = 13 m

Breadth of the rectangle = 7 m

Radius of the semi-circle = 3.5 m

We know two semi-circle = one circle

Hence, perimeter of the circle = 2 π r

                                            = 2 x 22/7 x 3.5 = 22 m

Perimeter of the rectangle = 2 (l + b)

                                       = 2 (13 + 7) = 40 m

Hence, perimeter of the garden = (22 m + 40 m) = 62 m

Now, area of the rectangle = 13 x 7 = 91 m²

Area of the circle (two semi-circles) = π r² 22/7 x 3.5 x 3.5 = 38.5 m²

Hence, Area of garden = 38.5 m² + 91 m² = 129.5 m²   

Q. 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 parallelogram = base × height

So, area of each tile = 24 × 10 = 240 cm²

Area of the floor = 1080 m² = (1080 x 100 x 100) cm²

Q. 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, circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.

Solution:

Therefore, the ant will have to take a longer round for the food-piece (b), because the perimeter of the figure given in alternative (b) is the greatest among all.