Question

In the given figure $O$ is centre of circular arc and $AOB$ is straight line find the area of the shaded region. Given $AC=12cm$ & $BC=16cm$

Answer 1

$AC=12cmBC=16cm$

The angle subtended by diameter is ${90}^{\circ }$

So the diameter is

$\sqrt{{12}^2+{16}^2}\sqrt{144+256}=\sqrt{400}=20$

So the radius of semicircle is $10cm$

Area of semicircle is

$=\frac{\pi r^2}{2}=\frac{22}{7}\times \frac{1}{2}\times {10}^2=157.14c{m}^2$

Area of triangle is

$\frac{1}{2}\times 12\times 16=96c{m}^2$

The area of shaded region is $157.14-96=61.14c{m}^2$