Question

In the given figure $DC=CB=4cm$ and $AE=2cm$. Calculate the area of shaded portion, if $DC\parallel AB$

• A. $8c{m}^2$
• B. $8.44c{m}^2$
• C. $7c{m}^2$
• D. $7.44c{m}^2$

Answer 1

The correct option is D $7.44c{m}^2$

R.E.F image

$ar\left(AECD\right)ar\left(ABCD\right)-ar\left(BCE\right)$

$\Rightarrow \frac{1}{2}(6+4)\times 4-\frac{\pi \times 4^2}{4}$

$\Rightarrow 20-12.56=7.44c{m}^2$

$ar\left(ABCD\right)=\frac{1}{2}\left(sumofparallelsides\right)\times htar\left(BCE\right)=\left(\frac{\theta }{{360}^o}\right)\left(\pi r^2\right)$