1. Let the right quadrilateral prism $A B C D-A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ have a rhombus as its base, with a base area of $2 \sqrt{3}, \angle A B C=60^{\circ}, E, F$ being points on the edges $C C^{\prime}, B B^{\prime}$ respectively, and $E C=B C=2 F B$, then the volume of the quadrilateral pyramid $A-B C E F$ is
A. $\sqrt{3}$
B. $\sqrt{5}$
C. 6
D. 9
1. Take the midpoint $K$ of $BC$ on the base $ABCD$, and connect $AK$.

Then $AK \perp BC$. Since $ABCD-A'B'C'D'$ is a right prism, $BB' \perp$ plane $ABCD$, thus $AK \perp BB'$.
Therefore, $AK \perp$ plane $BCEF$.
Since $S_{\text{trapezoid } ABCD}=BC^2 \sin 60^{\circ}=2 \sqrt{3}$,
we have $BC=AB=AC=2, AK=\sqrt{3}, CE=2, BF=1$.
Thus, $V_{A-BCFE}=\frac{1}{3} S_{\text{trapezoid } EFCB} \cdot AK=\sqrt{3}$.