Let $ABCD$ be a parallelogram of area $124\ cm^2$. If $E$ and $F$ are the mid-points of sides $AB$ and $CD$ respectively, then find the area of parallelogram $AEFD$.
Given:
$ABCD$ is a parallelogram of area $124\ cm^2$.
$E$ and $F$ are the mid-points of sides $AB$ and $CD$ respectively.
To do:
We have to find the area of parallelogram $AEFD$.
Solution:
Area of parallelogram $ABCD = 124\ cm^2$
Join $E$ and $F$.
Draw $DL \perp AB$
Area of parallelogram $ABCD = Base \times Altitude$
$= AB \times DL$
$= 124\ cm^2$
$E$ and $F$ are the mid points of sides $AB$ and $CD$.
This implies,
$AEFD$ is a parallelogram.
Area of parallelogram $AEFD = AE \times DL$
$=\frac{1}{2}\times AB \times DL$
$= \frac{1}{2}\times Area of ABCD$
$=\frac{1}{2}\times 124$
$=62\ cm^2$
The area of parallelogram $AEFD$ is $62\ cm^2$.
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