Question

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

Answer 1

Let 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 = a² + a²

64 = 2a²

a² = 32

Hence,

Area of square = a²

= 32 cm²

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

∴ Area of the circle = πr²

= π(4)²

= 16 cm²

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

The area of the shaded region = 16π – 32

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

= `128/7`

= 18.286 cm²