Question 12
Let $ABC$ be a triangle and let $D$, $E$ and $F$ be points on the segments $AC$, $BA$ and $CB$ respectively, such that the segments $AF$, $BD$, $CE$ meet at a point $P$ in the interior of the triangle. We know that $BP = 6$, $PD = 6$, $PC = 9$, $PE = 3$ and $AF = 20$. Find the area of the triangle $ABC$.