Question 5
The base of a right prism is a rhombus $ABCD$ of side $a$ and acute angle $60^\circ$. Join $B'$ to the midpoint $M$ of $AD$, and $D'$ to the midpoint $N$ of $AB$. The lines $B'M$ and $D'N$ intersect and form angle $B'OD'=\alpha$. Find the prism's volume.