Given that a generic $n$-gon ($n\geq3$) is inscribed in a circle in $\mathbb{R}^2$, we know the lengths of all its edges $a_1,a_2,\cdots,a_n$. Are there formulae to calculate its area (under Euclidean metric)?
For $n=3$, let $p=\frac{\sum_{i\in [n]} a_i}{2}$, we have the Heron's formula: $$A=\sqrt{p(p-a_1)(p-a_2)(p-a_3)}$$ which is the special case of the following $n=4$ formula ($a_4=0$): $$ A=\sqrt{(p-a_1)(p-a_2)(p-a_3)(p-a_4)}.$$ Are there any known result for $n\geq 5$?
If not, any proof that certain formulae don't exist?