Question

In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.

Answer 1

Let us take a be the side of square.

Diameter of a circle = Diagonal of the square = 8 cm

In right angled triangle ABC,

Using Pythagoras theorem,

`(AC)^2 = (AB)^2 + (BC)^2`

`(8)^2 = a^2 + a^2`

`64 = 2a^2`

`a^2 = 32`

Area of square = a²

= 32  cm²

Radius of the circle = `"Diameter"/2`

Area of the circle = `pir^2`

= `pi(4)^2`

= 16 cm²

So, the area of the shaded region = Area of circle – Area of square

The area of the shaded region = `16pi - 32`

= `16 xx (22/7) - 32`

= `128/7`

= 18.286 cm²