The Quadrilateral of Centroids
Let ABCD be a quadrilateral and E, F, G and H be the centroids of the triangles ABC, BCD, ACD, and ABD. Then 9×area(EFGH) = area(ABCD). Also EF AD, FG AB, GH BC and EH CD.
The statement of the theorem is in Problem 98. Quadrilateral Areas, Centroids, Similarity.