Question

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

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

Answer 1

Answer: (C)

$48{cm}^2$

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

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

$\Rightarrow$ So, we know that parallelograms 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 ( 1 ) we get,

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