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)