Question

$PQRS$ and $ABRS$ are parallelograms and $X$ is any point on the side $BR$. Show that $ar\left(PQRS\right)=ar\left(ABRS\right)$

Answer 1

Since $PQRS$ is a parallelogram

$PQ||RS$ (opposite sides of parallelogram are parallel)

And $ABRS$ is also a parallelogram

So, $AB||RS$ (opposite sides of parallelogram are parallel)

Since $PQ||RS$ and $AB||RS$

We can say that $PB||RS$

Now, $PQRS$ and $ABRS$ are two parallelograms with the same base RS and between the same parallels $PB$ and $RS$

Therefore, $ar\left(PQRS\right)=ar\left(ABRS\right)$