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 S1. Prove that \({S_1} = {7 \over 25}{S}\).

Geometry Problem 1494: Parallelogram, Midpoints, Octagon, Areas