Geometry Problem 1494: Parallelogram, Midpoints, Octagon, Areas

The figure below shows
a parallelogram ABCD with M, N, P, and Q midpoints of AB, BC, CD, and AD.
Lines AN, AP, BP, BQ, CM, CQ, DM, and DN determine the octagon EFGHIJKL of
area S_{1}. Prove
that \({S_1} = {7 \over 25}{S}\).