Question 15
Given a convex hexagon, take the midpoint of each of the six diagonals joining vertices which are separated by a single vertex (so if the vertices are in order $A$, $B$, $C$, $D$, $E$, $F$, then the diagonals are $AC$, $BD$, $CE$, $DF$, $EA$, $FB$). Show that the midpoints form a convex hexagon with a quarter the area of the original.