Question

Find the area of the shaded region in the given figure where $PQRS$ is a square of side $12cm$ and $A,B,C$ and $D$ are mi-points of the sides $PQ,QR,RS$ and $PS$.

Answer 1

Let A be the area of shaded region and B be the area of one quarter circle.

$4B=$ Area of circle of radius $6$

$=\pi (6{)}^2=36\pi$

$A+4B=$ Area of PQRS(square)

$\Rightarrow A+36\pi ={12}^2=144$

$\therefore A=144-36\pi c{m}^2$

So, area of shaded region$=144-36\pi c{m}^2$