CAT 2020 Quant Question [Slot 3] with Solution 20

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

Option: 28
Solution:

Dropping a perpendicular DE onto AB, the figure is divided into two parts - a rectangle of dimensions \(4 \times 5\) and an isosceles triangle AED.

Required answer = Area of rectangle + Area of triangle \( = 4 \times 5 + \frac{1}{2}(4 \times 4) = 28c{m^2}\)

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