question_answer

ABCD is a trapezium with AD and BC parallel sides. E is a point on BC. The ratio of the area of ABCD to that of AED is

A) \[\frac{\overline{AD}}{\overline{BC}}\]

B) \[\frac{\overline{BE}}{\overline{EC}}\]

C) \[\frac{\overline{AD}+\overline{BE}}{\overline{AD}+\overline{CE}}\]

D) \[\frac{\overline{AD}+\overline{BC}}{\overline{AD}}\]

Correct Answer: D

Solution :

[d] Area of trapezium \[ABCD=\frac{1}{2}\times (AD+BC)\times AE\] Area of \[\Delta AED=\frac{1}{2}\times AE\times AD\] \[\therefore \]Required ratio \[=\frac{\frac{1}{2}(AD+BC)\times AE}{\frac{1}{2}\times AE\times AD}\] \[=\frac{\overline{AD}+\overline{BC}}{\overline{AD}}\]