Point $$P^{}_{}$$ is inside $$\triangle ABC^{}_{}$$. Line segments $$APD^{}_{}$$, $$BPE^{}_{}$$, and $$CPF^{}_{}$$ are drawn with $$D^{}_{}$$ on $$BC^{}_{}$$, $$E^{}_{}$$ on $$AC^{}_{}$$, and $$F{}{}^{}_{}$$ on $$AB^{}_{}$$ (see the figure at right). Given that $$AP=6^{}_{}$$, $$BP=9^{}_{}$$, $$PD=6^{}_{}$$, $$PE=3^{}_{}$$, and $$CF=20^{}_{}$$, find the area of $$\triangle ABC^{}_{}$$.

(第七届AIME1989 第15题)