Difference between revisions of "Brahmagupta's Formula"

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'''Brahmagupta's formula''' is a [[formula]] for determining the [[area]] of a [[cyclic quadrilateral]] given only the four side lengths.
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'''Brahmagupta's Formula''' is a [[formula]] for determining the [[area]] of a [[cyclic quadrilateral]] given only the four side [[length]]s.
  
 
== Definition ==
 
== Definition ==
  
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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Given a cyclic quadrilateral with 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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<cmath>K = \sqrt{(s-a)(s-b)(s-c)(s-d)}</cmath>
  
<math>{K = \sqrt{(s-a)(s-b)(s-c)(s-d)}}</math>
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where <math>s=\frac{a+b+c+d}{2}</math> is the [[semiperimeter]] of the quadrilateral.
  
  
where the [[semiperimeter]] <math>s=\frac{a+b+c+d}{2}</math>.
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===Proof===
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{{incomplete|proof}}
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== Similar formulas ==
 
== Similar formulas ==

Revision as of 13:33, 6 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 with side lengths ${a}$, ${b}$, ${c}$, ${d}$, the area ${K}$ can be found as:

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

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


Proof

Template:Incomplete


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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