CMO 1994 Problem 1

Let $ABCD$ be a trapezoid with $AB\parallel CD$ . Points $E,F$ lie on segments $AB,CD$ respectively. Segments $CE,BF$ meet at $H$ , and segments $ED,AF$ meet at $G$ . Show that $S_{EHFG}\le \dfrac{1}{4}S_{ABCD}$ . Determine, with proof, if the conclusion still holds when $ABCD$ is just any convex quadrilateral.