Question

Let $ABCD$ be a parallelogram of area $124c{m}^2$. If $E$ and $F$ are the mid-points of sides $AB$ and $CD$ respectively, then find the area of parallelogram $AEFD$.

Answer 1

Given:

$ABCD$ be a parallelogram and area of parallelogram is $124c{m}^2$

Construction: Drop perpendicular $AP$ to side $CD$

Now, Area of parallelogram $EBCF=FC\times AP$ and Area of parallelogram $AEFD=DF\times AP$

Since $F$ is the mid-point of $DC$, so $DF=FC$

$\Rightarrow$ Area of parallelogram $AEFD=$Area of parallelogram $EBCF=\frac{1}{2}$ (Area of parallelogram $ABCD$)

$=\frac{124}{2}$

$=62$

Hence, the required area is $62c{m}^2$.