Question 72
Let $ABCDEF$ be a convex hexagon of area $1$ whose opposite sides are parallel. The lines $AB$, $CD$ and $EF$ meet in pairs to determine the vertices of a triangle. Similarly, the lines $BC$, $DA$ and $FA$ meet in pairs to determine the vertices of another triangle. Show that the area of the least one of these two triangles is at least $\frac{3}{2}$.