CAT 2022 Slot 1 QA Question 11: A trapezium ABCD has side AD parallel to BC, $\angle BAD = 90^\circ$, BC = $3$ cm and AD = $8$ cm. If the perimeter of this trapezium is $36$ cm, then its area, in sq. cm, is

Question

A trapezium ABCD has side AD parallel to BC, $\angle BAD = 90^\circ$, BC = $3$ cm and AD = $8$ cm. If the perimeter of this trapezium is $36$ cm, then its area, in sq. cm, is

Accepted Answer

Let $AB = h$ be the height of the trapezium. Since AD and BC are parallel and $\angle BAD = 90^\circ$, the horizontal difference between the other endpoints of the parallel sides is $8 - 3 = 5$ cm.
$CD = \sqrt{h^2 + 5^2} = \sqrt{h^2 + 25}$
Using the perimeter,
$AB + BC + CD + AD = 36$
$\Rightarrow h

A trapezium ABCD has side AD parallel to BC, ∠BAD=90∘\angle BAD = 90^\circ∠BAD=90∘, BC = 333 cm and AD = 888 cm. If the perimeter of this trapezium is 363636 cm, then its area, in sq. cm, is

A trapezium ABCD has side AD parallel to BC, $\angle BAD = 90^\circ$ , BC = $3$ cm and AD = $8$ cm. If the perimeter of this trapezium is $36$ cm, then its area, in sq. cm, is