Question

$OA$ and $OB$ are two mutually perpendicular radii of a circle with radius $10.5cm$. $D\in OB$ and $OD=6cm$. Find the area of the shaded region in the figure given below:

Answer 1

For sector $OACB$, radius $r=10.5cm=\frac{21}{2}cm$ and the measure of the angle $\theta ={90}^o$
In $△AOD,OA=10.5cm$ and altitude $OD=6cm$.
Area of the coloured region= Area of sector $OACB$ $-$ Area of $△AOD$
$=\frac{\pi r^2\theta }{360}-\frac{1}{2}\times OA\times OD$
$=\frac{22}{7}\times \frac{21}{2}\times \frac{21}{2}\times \frac{90}{360}-\frac{1}{2}\times 10.5\times 6$
$=86.625-31.5$
$=55.125{cm}^2$