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