CAT 2020 Slot 3 QA Question 5: In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and $\angle BAD = 45^\circ$. If DC = 5 cm, BC = 4 cm, the area of the trapezium in sq cm is

Question

In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and $\angle BAD = 45^\circ$. If DC = 5 cm, BC = 4 cm, the area of the trapezium in sq cm is

Accepted Answer

Since AB is parallel to DC and BC is perpendicular to DC, the height of the trapezium is $BC = 4$ cm.
At A, the slanted side makes $45^\circ$ with AB. Therefore, the horizontal extra length equals the vertical height, i.e., 4 cm.
So, $AB = DC + 4 = 5 + 4 = 9$ cm
Area of trapezium = $\dfrac{1}{2} 	i

In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and ∠BAD=45∘\angle BAD = 45^\circ∠BAD=45∘. If DC = 5 cm, BC = 4 cm, the area of the trapezium in sq cm is

In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and $\angle BAD = 45^\circ$ . If DC = 5 cm, BC = 4 cm, the area of the trapezium in sq cm is