AT-OEMO-FED1 2003 Problem 4

In a parallelogram $ABCD$ , points $E$ and $F$ are the midpoints of $AB$ and $BC$ , respectively, and $P$ is the intersection of $EC$ and $FD$ . Prove that the segments $AP,BP,CP$ and $DP$ divide the parallelogram into four triangles whose areas are in the ratio $1 : 2 : 3 : 4$ .