Problem #PRU-5207

Problem

A quadrilateral $ABCD$ is given. Point $M$ is a midpoint of $AB$ and point $N$ is a midpoint of $CD$. Point $P$ is where segments $AN$ and $DM$ meet, point $Q$ is where segments $MC$ and $NB$ meet. Show that the sum of areas of triangles $APD$ and $BCQ$ is equal to the area of the quadrilateral $MQNP$.