Question

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

Answer 1

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

Required answer = $\text{Area of rectangle} + \text{Area of triangle}$

= $4×5+\frac{1}{2}(4×4)=28\;cm^2$