Difference between revisions of "Bretschneider's formula"
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| − | Suppose we have a [[quadrilateral]] with [[side]]s of length <math>a,b,c,d</math> and [[diagonal]]s of length <math>p, q</math>. '''Bretschneider's formula''' states that the [[area]] | + | Suppose we have a [[quadrilateral]] with [[side]]s of length <math>a,b,c,d</math> (in that order) and [[diagonal]]s of length <math>p, q</math>. '''Bretschneider's formula''' states that the [[area]] |
<math>[ABCD]=\frac{1}{4}*\sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2}</math>. | <math>[ABCD]=\frac{1}{4}*\sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2}</math>. | ||
Revision as of 15:47, 31 July 2006
Suppose we have a quadrilateral with sides of length 
(in that order) and diagonals of length 
. Bretschneider's formula states that the area
![$[ABCD]=\frac{1}{4}*\sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2}$](http://latex.artofproblemsolving.com/7/5/9/7596249e635c730943d0f5493ab8e0d9f2399293.png)
.
It can be derived with vector geometry.
See Also
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