AMC 10 2008a Problem 21

A cube with side length $1$ is sliced by a plane that passes through two diagonally opposite vertices $A$ and $C$ and the midpoints $B$ and $D$ of two opposite edges not containing $A$ or $C$, as shown. What is the area of quadrilateral $ABCD$?

$\mathrm{(A)}\ \frac{\sqrt{6}}{2} \mathrm{(B)}\ \frac{5}{4} \mathrm{(C)}\ \sqrt{2} \mathrm{(D)}\ \frac{5}{8} \mathrm{(E)}\ \frac{3}{4}$