ABCD is a trapezium with AD and BC parallel sides. The ratio of the area of ABCD to that of ΔAED is

ABCD is a trapezium with AD and BC parallel sides. The ratio of the area of ABCD to that of ΔAED is

Answer: Option D

Solution

Answer: Option D

Solution:

$$\begin{array}{rl}& \text{Let EN }\perp \text{AD}\\ & \text{Area of }\Delta \text{AED}=\frac{1}{2}\times \text{EN}\times \text{AD}\\ & \text{Area of trapezium ABCD}\\ & =\frac{1}{2}\left(\text{AD}+\text{BC}\right)\times \text{EN}\\ & \frac{\text{ar}\left(\text{ABCD}\right)}{\text{ar}\left(\text{AED}\right)}\\ & =\frac{\frac{1}{2}\left(\text{AD}+\text{BC}\right)\times \text{EN}}{\frac{1}{2}\times \text{EN}\times \text{AD}}\\ & =\frac{\text{AD}+\text{BC}}{\text{AD}}\end{array}$$