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Chapter 11 Mensuration Ex 11.1 Solutions

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?

Answer - 1 : -

Perimeter of figure (a) = 4 × side = 4 × 60 = 240 m

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

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.

Answer - 2 : -

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 = 625m2 –300 m2 =325 m2
Cost of developing the garden = ₹ 325 × 55 = ₹ 17875

Question - 3 : -

The shape of a garden isrectangular 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]

Answer - 3 : -

Given: Total length = 20 m

Diameter of semi circle = 7 m

Radius of semi circle = 7/2 = 3.5 m

Length of rectangular field

= 20-(3.5+3.5) = 20-7 = 13 m

Breadth of the rectangular field = 7 m

Area of rectangular field = l×b

= 13×7= 91m2

Area of two semi circles = 2×(1/2)×π×r2

= 2×(1/2)×22/7×3.5×3.5

= 38.5 m2

Area of garden = 91+38.5 = 129.5 m2

Now Perimeter of two semi circles =  2πr = 2×(22/7)×3.5 = 22 m

And Perimeter of garden = 22+13+13

= 48 m. Answer

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).

Answer - 4 : -

Area of the floor = 1080 m2 =1080 × 10000 cm2 =10800000 cm2 [∵ 1 m2 =10000 cm2]
Area of 1 tile = 1 × base × height = 1 × 24 × 10 = 240 cm2
Number of tiles required

= 45000 tiles

 

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.

Answer - 5 : -



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