2018 AMC 12B Problem #13

Square $ABCD$ has side length 30. Point $P$ lies inside the square so that $AP = 12$ and $BP = 26.$ The centroids of $\triangle ABP,$ $\triangle BCP,$ $\triangle CDP,$ and $\triangle DAP$ are the vertices of a convex quadrilateral. What is the area of that quadrilateral?

This problem is part of the 2018 AMC 12B .