Problem 24 (2018 AMC 8)

In the cube $ABCDEFGH$ with opposite vertices $C$ and $E$, $J$ and $I$ are the midpoints of edges $\overline{FB}$ and $\overline{HD}$ respectively. Let $R$ be the ratio of the area of the cross-section $EJCI$ to the area of one of the faces of the cube. What is $R^2$? [See figure in original PDF]