Question

In the given figure, area of the parallelogram $ABCD$ is $48$ $c{m}^2$ and $FC\parallel AB$. Find the area of the parallelogram $ABEF$.

• A. $12c{m}^2$
• B. $24c{m}^2$
• C. $48c{m}^2$
• D. $8c{m}^2$

Answer 1

The correct option is C $48c{m}^2$

$\Rightarrow$ In given figure, we can see that parallelogram $ABCD$ and parallelogram $ABEF$ both are lies between same parallel line that is $FC$ and $AB$.

$\Rightarrow$ And parallelogram $ABCD$ and $ABEF$ contains same base that is $AB$.

$\Rightarrow$ So, we know that parallelogram on same base and between same parallels are equal in area.

$\Rightarrow$ So, $Area\left(ABCD\right)=Area\left(ABEF\right)$ ------ ( 1 )

$\Rightarrow$ We have given $Area\left(ABCD\right)=48c{m}^2$

From $\left(1\right)$ we get,

Area of parallelogram $ABEF=48c{m}^2$