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

Explanation

Let the side of a square be a and the radius of circle be r.
Given that, length of diagonal of square = 8cm
`rArr asqrt(2)=8`
`rArr a = 4sqrt(2)cm`
Now, Diagonal of a square = Diameter of a circle
`rArr` Diameter of circle = 8
`rArr` Radius of circle = r = `("Diameter")/(2)`
`rArr r= (8)/(2)=4cm`
`:.` Area of circle = `pir^(2) = pi(4)^(2)`
= `16pixxcm^(2)`
and Area of square = `a^(2) = (4sqrt(2))^(2)`
`32cm^(2)`
So, the area of the shaded region = Area of circle- Area of square
= `(16pi-32)cm^(2)`
Hence, the required area of the shaded region is `(16pi-32)cm^(2)`