Difference between revisions of "Brahmagupta's Formula"
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=== Similar formulas === | === Similar formulas === | ||
| − | [[Bretschneider's formula]] gives a formula for the area of a non-cyclic quadrilateral given only the side lengths; applying [[Ptolemy's | + | [[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>. | ||
Revision as of 12:54, 28 June 2006
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 
.
