question_answer

It ABCD is a rectangle, E, F are the mid-points of BC and AD, respectively and G is any point on EF, then what will be the area of AGAB ?

A) Area of rectangle ABCD

B)  \[\frac{1}{2}\]area of rectangle ABCD

C)  \[\frac{1}{4}\] area of rectangle ABCD

D)  None of the above

Correct Answer: C

Solution :

\[\because \]AB || EF || CD. So, ABEF is a rectangle.

\[\therefore \]Area of\[\Delta AGB=\frac{1}{2}\] (Area of rectangle ABEF)

\[\therefore \]      \[=\frac{1}{2}\times \left( \frac{1}{2}\times \text{Area of rectangle ABCD} \right)\]

\[=\frac{1}{4}\times \](Area of rectangle ABCD)