Let $ABCDEF$ be a straight triangular prism with all its congruent edges and its $AD, BE$, and $CF$ side edges. let $O $ and $O ' $ baricenters of bases $ABC$ and $DEF,$ respectively, and $P$ be a point belonging to $OO'$ such that $PO '= \frac {1} {6} OO'$. Let $ \pi$ be the plane determined by $P$ and the midpoints of $AB$ and $DF$. The $\pi$ plane divides the prism into two solids. Determine the ratio of the volume of the smallest solid to the volume of the largest solid, determined by the plane $\pi$
My attempt: Let $ M $ and $ N '$ be the midpoints of $ AB $ and $ DF $, respectively. The plan $ \pi $ is determined by the points $ P, M $ and $ N '$.
Let's identify the intersection of $ \pi $ with the edges of the prism. Points $ M $ and $ P $ belong to the $ MCFM '$ plan. The line determined by $ MP $ is not parallel to the line determined by $ CF $ and are coplanar so they are competing at one point $ V $
An issue that seems to be very laborious. I will wait for a solution soon. thank you soon!