OMCC 2000 Problem 3

Let $ABCDE$ be a convex pentagon. If $P$ , $Q$ , $R$ and $S$ are the respective centroids of the triangles $ABE$ , $BCE$ , $CDE$ and $DAE$ , show that $PQRS$ is a parallelogram and its area is $2/9$ of that of $ABCD$ .