Question

The area of the parallelogram ABCD is 90 cm(see Fig.5) Find
(i) ar (ABEF)
(ii) ar (ABD)

Answer 1

$\left(i\right)$ Here, $ABCD$ is a parallelogram.

$\therefore$ $AB\parallel CD$

So, $AB\parallel CF$ [ Extended part of parallel lines ]

$\therefore$ $AB\parallel EF$

Hence, $ABEF$ is a parallelogram.

Parallelogram $ABCD$ and parallelogram $ABEF$ lies between same parallel lines $AB$ and $CF$, having same base $AB$.

We know Parallelograms lies between same parallel lines and having same base are having equal areas.

$\therefore$ $ar\left(ABCD\right)=ar\left(ABEF\right)$

$\therefore$ $ar\left(ABEF\right)=90c{m}^2$

$\left(ii\right)$ $△ABD$ and parallelogram $ABCD$ lies between same parallel lines and having same base $AB$

$\therefore$ $ar\left(ABD\right)=\frac{1}{2}\times ar\left(ABCD\right)$

$\Rightarrow$ $ar\left(ABD\right)=\frac{1}{2}\times 90c{m}^2$

$\therefore$ $ar\left(ABD\right)=45c{m}^2$