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# 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.

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#### 2 comments

msh210‭ 8 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 5 months ago

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