MathNet 2015-part-03 — 191 problems (EN–VI) Question 15

Let $A B C D$ be a convex quadrilateral. Let $P, Q, R$ and $S$ be the midpoints of the sides $[A B],[B C],[C D]$ and $[D A]$. Show that the area of $PQRS$ is equal to half the area of $A B C D$.