AMC 8 2018 Problem 24

In the cube $ABCDEFGH$ with opposite vertices $C$ and $E,$ $J$ and $I$ are the midpoints of segments $\overline{FB}$ 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 $R^2?$

$\textbf{(A) } \frac{5}{4} \textbf{(B) } \frac{4}{3} \textbf{(C) } \frac{3}{2} \textbf{(D) } \frac{25}{16} \textbf{(E) } \frac{9}{4}$