Question

In the figure, point $D$ is the mid point of side $BC$ and point $G$ is the centroid of $\Delta ABC.$
Find $\frac{A\left(\Delta AGB\right)}{A\left(\Delta ABD\right)}.$

Answer 1

In the figure,

D is the mid point of side BC.

Hence, BD $=$ CD

G is the centroid of triangle ABC.

As we know centroid divide median in $2:1$ ratio

Hence, AG $:$ GD $=2:1$

If two triangles have same base of line and common vertex then their ratio of their area is equal to their base ratio.

$\frac{A\left(\Delta AGB\right)}{A\left(\Delta ABC\right)}=\frac{AG}{AD}$

$\Rightarrow \frac{A\left(\Delta AGB\right)}{A\left(\Delta ABC\right)}=\frac{2}{3}$.