Question

In $△ABC$, $E$ is mid-point of side $AB$ and $EBCD$ is a parallelogram. If the area of $△ABC$ is $80c{m}^2$, find the area of parallelogram $EBCD$.

• A. $80c{m}^2$
• B. $70c{m}^2$
• C. $60c{m}^2$
• D. $40c{m}^2$

Answer 1

The correct option is A $80c{m}^2$

$ABC$ is a $△$ and $E$ is the midpoint of $AB$.
$\therefore$ $AE=EB=\frac{AB}{2}$ $\left(1\right)$
Let $EC$ be the altitude from $C$ to $AB$
$\therefore$ Area of $△ABC=\frac{1}{2}\times AB\times EC$
$=EB\times EC$ (from $\left(1\right)$)
$=80c{m}^2$
Now,
Area of parallelogram $=EB\times EC$
$=80c{m}^2$