Let be a convex quadrilateral and points and on sides such that If is the area of show that .
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 $S\leq\frac{AB\cdot CD+n(n-1)AD^2+n^2DA\cdot BC}{2n^2}$.
Školjka 
be a convex quadrilateral and points 
and 
on sides 
such that
If 
is the area of 
show that 
.