Difference between revisions of "Brahmagupta's Formula"
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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 
, the area 
can be found as:
where the semiperimeter 
.
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 
.
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