1989 AIME Problem 15

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^{}_{}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.