Question

In given figure, OABC is square of side $7$ cm. If OAPC is a quadrant of a circle with center O, then the find the area of the shaded region. (Use $\pi$ $=\frac{22}{7}$).

Answer 1

$\Rightarrow$ Side of square $=7cm$

$\Rightarrow$ Area of square $OABC=(side{)}^2=(7{)}^2=49c{m}^2$

$\Rightarrow$ Here, radius of sector $r=7cm$ and $\theta ={90}^o$

$\Rightarrow$ Area of sector $OAPC=\frac{\theta }{{360}^o}\pi r^2$

$\Rightarrow$ Area of sector $OAPC=\frac{{90}^o}{{360}^o}\times \frac{22}{7}\times (7{)}^2$

$\therefore$ Area of sector $OAPC=\frac{22\times 49}{4\times 7}=38.5c{m}^2$

$\Rightarrow$ Area of shaded region = Area of square $OABC$ - Area of sector $OAPC$

$\therefore$ Area of shaded region $=49-38.5=10.5c{m}^2$