Question

Find the area of shaded region if $AE=9cm$, $\angle AED={90}^{\circ }$, $DE=12cm$.

Answer 1

$AD=\sqrt{9^2+9^2}=\sqrt{81+81}=\sqrt{162}$

$=9\sqrt{2}cm$

$\therefore$ Area of shaded region

$=Ar(semi-circle)+Ar\left(rectangle\right)-ar\left(\Delta AED\right)$

$=\frac{\pi r^2}{2}+l\times B-\frac{1}{2}\times b\times h$

$=\frac{3.14\times \frac{9}{\sqrt{2}}\times \frac{9}{\sqrt{2}}}{2}+12\times 9\sqrt{2}-\frac{1}{2}\times 9\times 9=63.58+152.28-40.5$

$=175.36c{m}^2$