# 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 11:54, 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 .