Question

If $G$ is the centroid of the triangle $ABC$, then area of $\Delta AGB=$

• A. Area of $\Delta ABC$
• B. $\frac{1}{3}$ area of $\Delta ABC$
• C. $3$ area of $\Delta ABC$
• D. $4$ area of $\Delta ABC$

Answer 1

The correct option is B $\frac{1}{3}$ area of $\Delta ABC$

If $G$ is the centroid of the triangle $△ABC$
Then $Area△AGB=Area△AGC=Area△CGB$
Now $Ar△AGB+Ar△AGC+Ar△CGB=Ar△ABC$
$\therefore 3Ar△AGB=Ar△ABC$
Hence, $Ar△AGB=\frac{1}{3}Ar△ABC$
Therefore, $Ar△AGB=Ar△AGC=Ar△CGB=\frac{1}{3}ar△ABC$