I have some troubles with this problem :
Let $ABCD$ be a convex quadrilateral. $M$, $N$, $P$ and $Q$ are the midpoints of the sides $AB$, $BC$, $CD$ and $AD$. $AN$, $BP$, $MD$ and $CQ$ are interescting in $X$, $Y$, $Z$ and $T$ like in the figure below. Prove that $[XYZT] = [AMX] + [BYN] + [CZP] + [DTQ]$. It is noted with $[ABC]$ the area of $ΔABC$.
Since $M$, $N$, $P$ and $Q$ are midpoints, the first thing that came in my mind was the median property : the median divides a triangle in two echivalent triangles (with the same area).
I would appreciate some suggestions.