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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