Question

In the figure alongside, $OAB$ is a quadrant of a circle. The radius $OA=3.5cm$ and $OD=2cm$. Calculate the area of the shaded portion. $(\text{Take}\pi =\frac{22}{7})$

Answer 1

Radius of quadrant $OACB,r=3.5cm$

$\therefore$ Area of quadrant $OACB=\frac{1}{4}\pi r^2$
$=\frac{1}{4}\times \frac{22}{7}\times 3.5\times 3.5=9.625c{m}^2$
Here, $\angle AOD={90}^{\circ }$
Then area of $\Delta AOD=\frac{1}{2}\times$ base $\times$ height$
Base $=3.5cm$ and height $=2cm$

$\therefore =\frac{1}{2}\times 3.5\times 2=3.5c{m}^2$
Area of shaded portion $=$ Area of quadrant $-$ Area of triangle
$=9.625-3.5$
$=6.125c{m}^2$.