Let $ABCD$ be a convex quadrilateral whose diagonals $AC$ and $BD$ intersect at a point P. Let $M,N$ be the midpoints of the sides $AB$ and $CD$ respectively. Prove that the area of the triangle $PMN$ is equal to the quarter of the absolute value of the difference between the area of the triangle $DAP$ and the area of the triangle $BCP$: $$\text{area}(\triangle MNP)=\frac{1}{4}\left|\text{area}(\triangle DAP)-\text{area}(\triangle BCP)\right |.$$