Square A B C D has side length 30 . Point P lies inside the square so that A P=12 and B P=26. The centroids of \triangle A B P, \triangle B C P, \triangle C D P, and \triangle D A P are the vertices of a convex quadrilateral. What is the area of that quadrilateral?
Answer Choices
A. 100 \sqrt{2}
B. 100 \sqrt{3}
C. 200
D. 200 \sqrt{2}
E. 200 \sqrt{3}