Point P is inside \triangle A B C. Line segments \overline{A P D}, \overline{B P E} and \overline{C P F} are drawn with D on \overline{B C}, E on \overline{C A}, and F on \overline{A B} (see the figure at the right). Given that A P=6, B P=9, P D=6, P E=3 and C F=20, find the area of \triangle A B C.
