Brahmagupta's Formula

Revision as of 13:33, 6 August 2008 by JBL (talk | contribs)

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 with side lengths ${a}$, ${b}$, ${c}$, ${d}$, the area ${K}$ can be found as:

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

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


Proof

Template:Incomplete


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 ${d}=0$. This article is a stub. Help us out by expanding it.

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