Question 162
In $\triangle ABC$, $D$, $E$, $F$ are points on $BC$, $CA$ and $AB$ respectively such that the line segments $AD$, $BE$ and $CF$ meet at $G$. If the lengths of $DG$, $EG$, $BG$, $AG$ and $CF$ are $1$, $2$, $3$, $4$, $5$ respectively, find the area of $\triangle ABC$.