is there a formula for an upper bound for the area of a polygon, knowing the length of its edges? In the ideal situation, the answer would be a function $f_n(l_1,l_2,\dots,l_n)$ of the edges lengths (the number $n$ of edges is fixed).
In a less ideal situation, the answer would be a function $g_n(p)$ of the perimeter (one function for every parameter $n$) which give a better estimation than the isoperimetric inequality (cf. example below).
Isoperimetric inequality is not ideal as the following example shows: consider all parallelograms with sides $1$ and $a$. Then the maximum of area is $a$, obtained for the rectangle. But the isoperimetric inequality only gives $A\leqslant \frac{p^2}{4\pi}=\frac{(a+1)^2}{\pi}$.
Edit: by polygons, I mean convex polygons. But if there exists a formula for the convex and nonconvex case, it will be fine for me (I guess that nonconvex polygons tend to have a smaller area than convex ones).