The base of a a pyramid $ABCDM$ is a rectangle $ABCD$ with sides $4\sqrt2$ and $4$. The triangles $ACM$ and $BDM$ are equilateral. Find the volume of the pyramid $ABCDM$.
The volume is given by $$V=\dfrac13.B.H,$$ so we are supposed to find the height $H$ of the pyramid and the area $B$ of the parallelogram $ABCD$ which is the base. $$B=ab=4\times4\sqrt2=16\sqrt2.$$ I am pretty sure that the projection $O$ of the apex $M$ onto the plane of the base is actually the intersection of the diagonals of $ABCD$, but I don't see how to show that. Can you help me?