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?
(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.
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.
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).
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.
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.