Question

In given figure, PQRS is a square of side $4$ cm. Find the area of the shaded square.

Answer 1

$\Rightarrow$ Here, $r=1cm,\theta ={90}^o$ and $a=4cm$

$\Rightarrow$ Area of $4$ sectors $=4\times \frac{\theta }{{360}^o}\pi r^2$

$\Rightarrow$ Area of $4$ sectors $=4\times \frac{{90}^o}{{360}^o}\times 3.14\times (1{)}^2$

$\therefore$ Area of $4$ sectors $=\frac{4\times 3.14\times 1}{4}=3.14c{m}^2$

$\Rightarrow$ Area of circle $=\pi r^2=3.14\times (1{)}^2=3.14c{m}^2$

$\Rightarrow$ Area of a square $=a^2=(4{)}^2=16c{m}^2$

$\Rightarrow$ Area of shaded region $=$ Area of square - (Area of $4$ sectors + Area of circle)

$\Rightarrow$ Area of shaded region $=16-(3.14+3.14)$

$\therefore$ Area of shaded region $=16-6.28=9.72c{m}^2$