In the cube $ABCDEFGH$ with opposite vertices $C$ and $E$, a plane passes through $E$, $C$, and the midpoint of edge $\overline{AB}$. This plane intersects the cube to form a quadrilateral cross-section. Let $R$ be the ratio of the area of this cross-section to the area of one of the faces of the cube. What is $R^2$?