Difference between revisions of "Brahmagupta's Formula"

(Similar formulas)
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Brahmagupta's formula reduces to [[Heron's formula]] by setting the side length <math>{d}=0</math>.
 
Brahmagupta's formula reduces to [[Heron's formula]] by setting the side length <math>{d}=0</math>.
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[[Category:Geometry]]
 
[[Category:Geometry]]
 
{{stub}}
 
{{stub}}
 
[[Category:Theorems]]
 
[[Category:Theorems]]

Revision as of 14:18, 23 October 2007

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

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