Question 11
$ABCD$ is any convex quadrilateral. Construct a new quadrilateral as follows. Take $A'$ so that $A$ is the midpoint of $DA'$; similarly, $B'$ so that $B$ is the midpoint of $AB'$; $C'$ so that $C$ is the midpoint of $BC'$; and $D'$ so that $D$ is the midpoint of $CD'$. Show that the area of $A'B'C'D'$ is five times the area of $ABCD$.