Question

In the given figure, ABCD is the square of side 21 cm. AC and BD are two diagonals of the square. Two semicircles are drawn with AD and BC as diameters. Find the area of the shaded region. (Take `pi = 22/7`)

Answer 1

Area of one semi-circle = `1/2 xx pi xx (21/2)^2`

⇒ Area of both semi-circles = `2 xx 1/2 xx pi xx (21/2)^2`

Area of one triangle = `1/2 xx  21 xx 21/2`

⇒  Area of both triangles = `2 xx 1/2 xx 21 xx 21/2`

Area of shaded portion

`= 2 xx 1/2 xx pi xx (21/2)^2 + 2 xx 1/2  xx 21 xx 21/2`

`= 22/7 xx 441/4 + 441/2`

`= 693/2  + 441/2`

`= 1134/2`

`= 567 cm^2`