Question

$ABCD$ is a rectangle with sides $AB=x$ and $AD=y$. E is the mid point of $DC$. Then find the area of the shaded portion?

• A. $\frac{xy}{2}$
• B. $\frac{xy}{4}$
• C. $\frac{xy}{8}$
• D. none

Answer 1

The correct option is A $\frac{xy}{2}$

As ${}^{\prime }{E}^{\prime }$ is midpoint $\Rightarrow DE=EC=\frac{x}{2}$

$ABCD$ is a Rect $=\angle D=\angle C={90}^{\circ }$

$\Rightarrow$ as $\left(ABE\right)=as\left(ABCD\right)-as\left(ADE\right)-as\left(BEC\right)$

$\Rightarrow as\left(ABE\right)=xy-(\frac{1}{2}\times y\times \frac{x}{2})-(\frac{1}{2}\times y\times \frac{x}{2})$

$\Rightarrow as\left(ABE\right)=xy-\frac{xy}{2}=\frac{xy}{2}$