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:
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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>
  
<math>K = \sqrt{(s-a)(s-b)(s-c)(s-d)}</math>
 
  
 
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 11:45, 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 ${a}$, ${b}$, ${c}$, ${d}$, the area ${K}$ can be found as:


${K = \sqrt{(s-a)(s-b)(s-c)(s-d)}}$


where the semiperimeter $s=\frac{a+b+c+d}{2}$.

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 ${d}=0$. This article is a stub. Help us out by expanding it.

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