Difference between revisions of "Brahmagupta's Formula"
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'''Brahmagupta's formula''' is a [[formula]] for determining the [[area]] of a [[cyclic quadrilateral]] given only the four side lengths. | '''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 <math>{a}, {b}, {c}, {d}</math>, the area <math>{K}</math> can be found as: | Given a cyclic quadrilateral has side lengths <math>{a}, {b}, {c}, {d}</math>, the area <math>{K}</math> can be found as: | ||
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where the [[semiperimeter]] <math>s=\frac{a+b+c+d}{2}</math>. | where the [[semiperimeter]] <math>s=\frac{a+b+c+d}{2}</math>. | ||
| − | + | == 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. | [[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 <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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| + | {{stub}} | ||
| + | [[Category:Geometry]] | ||
| + | [[Category:Theorem]] | ||
Revision as of 17:01, 7 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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