Question

In the adjoining figure, $ABCD$ is a rectangle of size $18cm$ by $10cm$. In $\Delta BEC,\angle E={90}^o$ and $EC=8cm$. Find the area of the shaded region.

Answer 1

In $△BCE$

$\Rightarrow E{B}^2+E{C}^2=B{C}^2$

$\Rightarrow E{B}^2=B{C}^2-E{C}^2$

$\Rightarrow EB=\sqrt{100-64}=\sqrt{36}=6cm$

Area of the $△EBC=\frac{1}{2}\times EB\times EC$

$=\frac{1}{2}\times 6cm\times 8cm=24c{m}^2$

Area of rectangle $ABCD=18cm\times 10cm=180c{m}^2$

Area(shaded region) $=ar$(rectangle)$-ar\left(△BCE\right)$

$180c{m}^2-24c{m}^2=156c{m}^2$