# Method to calculate the area of a cyclic n-gon

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The area of a cyclic quadriateral, given the side lengths, is given as follows: $$ \sqrt{(s-a)(s-b)(s-c)(s-d)} $$

(Brahmagupta's formula)

Where $ s = \frac{a+b+c+d}{2}. $

I want to find a similar expression, or a way of formulating an expression for a cyclic $n-gon$ given it's sides, since I want to implement it in a program.

## 2 comments

These may help: https://doi.org/10.1007/11615798_4 , https://arxiv.org/abs/math/0407300 — msh210 6 months ago

A cyclic $n$-gon can be broken into a bunch of disjoint cyclic triangles / quadrilaterals. This observation gives a simple algorithm to calculate the area of a cyclic $n$-gon. Note: this approach requires determining lengths of chords between vertices. — gramps 3 months ago