Point P is inside △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 △ABC.[asy]
size(200);
pair A=origin, B=(7,0), C=(3.2,15), D=midpoint(B--C), F=(3,0), P=intersectionpoint(C--F, A--D), ex=B+40*dir(B--P), E=intersectionpoint(B--ex, A--C);
draw(A--B--C--A--D^^C--F^^B--E);
pair point=P;
label("A", A, dir(point--A));
label("B", B, dir(point--B));
label("C", C, dir(point--C));
label("D", D, dir(point--D));
label("E", E, dir(point--E));
label("F", F, dir(point--F));
label("P", P, dir(0));[/asy] geometryratiosearchfunctionarea of a triangleHeron's formulaalgebra