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Brahmagupta's Formula

Revision as of 11:54, 28 June 2006 by Inscrutableroot (talk | contribs) (proofreading)

Brahmagupta's formula is a formula for determining the area of a cyclic quadrilateral given only the four side lengths.

Definition

Given a cyclic quadrilateral has side lengths ${a}, {b}, {c}, {d}$, the area ${K}$ can be found as:

$K = \sqrt{(s-a)(s-b)(s-c)(s-d)}$

where the semiperimeter $s=\frac{a+b+c+d}{2}$.

Similar formulas

Bretschneider's formula gives a formula for the area of a non-cyclic quadrilateral given only the side lengths; applying Ptolemy's Theorem to Bretschneider's formula reduces it to Brahmagupta's formula.

Brahmagupta's formula reduces to Heron's formula by setting the side length ${d}=0$.

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