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in Coordinate Geometry by (43.3k points)
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If G is the centroid of ΔABC, then ΔGAB = ……………….

A) \(\frac{1}{13}ar(\triangle ABC)\)

B) \(\frac{1}{4}ar(\triangle ABC)\)

C) \(\frac{1}{2}ar(\triangle ABC)\)

D)  \(\frac{1}{3}ar(\triangle ABC)\)

2 Answers

+1 vote
by (57.0k points)
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Best answer

Correct option is (D) \(\frac{1}{3}ar(\triangle ABC)\)

If G is centroid of the triangle ABC.

Then \(ar(\triangle GAB)=ar(\triangle GBC)=ar(\triangle GCA)\)

and \(ar(\triangle GAB)+ar(\triangle GBC)\) \(+ar(\triangle GCA)=ar(\triangle ABC)\)

\(\Rightarrow\) \(3ar(\triangle GAB)=ar(\triangle ABC)\)

\(\Rightarrow\) \(ar(\triangle GAB)=\frac{1}{3}ar(\triangle ABC)\)

+1 vote
by (43.0k points)
edited by

Correct option is  D)  \(\frac{1}{3}ar(\triangle ABC)\)

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