Question

find the area of the shaded region in the following figure

Answer 1

Answer:

259.875 m²

Step-by-step explanation:

Area of bigger circle = pie ×  (radius)²

Radius = Diameter/2

= (22/7) × (21/2)²

= (22/7) × (21/2) × (21/2)

= (11 × 3 × 21) /2

= 693/2

Area of two semicircles = area of one circle ( as semi circles are identical)

= (22/7) × (21/4)²

= (22/7) × (21/4) ×  (21/4)

= (11 × 3 × 21) /8

= 693/8

Area of shaded region = 693/2  - 693/8

= (693/8)(4-1)

= (693/8)×3

= 259.875 m²

Answer 2

It is given that the diameter of the big circle is 21 m

So, its radius=(Diameter/2) m=21/2m

Now, area of the big circle=πr²

=22/7×(21/2)²

=22/7×441/4

=693/2 m²

So, we have the area of the big circle as 693/2 m²

In the above given figure, there are 2 semi-circles of equal diameter 10.5 m, and when we join these 2 semi-circles, we get a circle.

Its radius=(Diameter/2) m=10.5/2 m

So, area of that circle=πr²

=22/7×(10.5/2)²

=22/7×441/16

=693/8 m²

Now, area of the remaining/shaded portion=Area of the big circle-Area of the circle obtained by joining two semi-circles in the above give picture.

=(693/2-693/8) m²

=2079/8 m²

=259.875 m²