Square ABCD has side length 30. Point P lies inside the square so that AP=12 and BP=26. The centroids of △ABP, △BCP, △CDP, and △DAP are the vertices of a convex quadrilateral. What is the area of that quadrilateral? [asy]
unitsize(120);
pair B = (0, 0), A = (0, 1), D = (1, 1), C = (1, 0), P = (1/4, 2/3);
draw(A--B--C--D--cycle);
dot(P);
defaultpen(fontsize(10pt));
draw(A--P--B);
draw(C--P--D);
label("A", A, W);
label("B", B, W);
label("C", C, E);
label("D", D, E);
label("P", P, N*1.5+E*0.5);
dot(A);
dot(B);
dot(C);
dot(D);
[/asy]
<spanclass=′latex−bold′>(A)</span>1002<spanclass=′latex−bold′>(B)</span>1003<spanclass=′latex−bold′>(C)</span>200<spanclass=′latex−bold′>(D)</span>2002<spanclass=′latex−bold′>(E)</span>2003