CAT 2021 Slot 2 QA Question 21: The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD

Question

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD

Accepted Answer

Let $AB = DP = x$, since ABPD is a parallelogram. Since P is the midpoint of CD, $CP = DP = x$. Therefore, $CD = 2x$.

Let the height of the trapezium be $h$.

$	ext{Area of parallelogram ABPD} = xh$
$	ext{Area of triangle BPC} = \dfrac{1}{2}xh$

The difference between these areas is 10 sq cm.
$xh

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is