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ABCD is a parallelogram of area S. E and F are the middle points of the sides AD and BC respectively. If G is any point on the line EF, then area of \( \Large \triangle AGB \) is equal to

A) \( \Large \frac{S}{2} \)
B) \( \Large \frac{S}{3} \)
C) \( \Large \frac{S}{4} \)
D) \( \Large \frac{3S}{4} \)

Correct Answer:



C) \( \Large \frac{S}{4} \)

Description for Correct answer:

Area of ABCD = S

Therefore, Area of ABFE = \( \Large \frac{1}{2}S \)

Since both \( \Large \triangle AGB\ and\ \triangle GFB \) stand on the same base and between same parallels, therefore

Area of AGB = \( \Large \frac{1}{2}\ area\ of\ AEFB \)

= \( \Large \frac{1}{2} \times \left[ \frac{1}{2}S \right] = \frac{S}{4} \)

Part of solved Mensuration questions and answers : >> Aptitude >> Mensuration

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