Školjka

Let $ABCD$ be a convex quadrilateral and points $E$ and $F$ on sides $\overline{AB},\overline{CD}$ such that\[\tfrac{AB}{AE}=\tfrac{CD}{DF}=n \text.\] If $S$ is the area of $AEFD$ show that $S\leq\frac{AB\cdot CD+n(n-1)AD^2+n^2DA\cdot BC}{2n^2}$.