# Difference between revisions of "Brahmagupta's Formula"

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== Definition == | == 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}</math>, <math>{b}</math>, <math>{c}</math>, <math>{d}</math>, the area <math>{K}</math> can be found as: |

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+ | <math>{K = \sqrt{(s-a)(s-b)(s-c)(s-d)}}</math> | ||

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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>. |

## Revision as of 12:45, 5 August 2008

**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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