Difference between revisions of "Bretschneider's formula"
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| − | Let us have a [[quadrilateral]] with side lengths <math>a,b,c,d</math>, and diagonals<math>p, q</math>. Bretschneider's formula says that | + | Let us have a [[quadrilateral]] with side lengths <math>a,b,c,d</math>, and diagonals <math>p, q</math>. Bretschneider's formula says that |
<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>. | ||
It is derived through [[vector]] geometry. | It is derived through [[vector]] geometry. | ||
Revision as of 17:41, 21 June 2006
Let us have a quadrilateral with side lengths 
, and diagonals 
. Bretschneider's formula says that
![$[ABCD]=\frac{1}{4}*\sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2}$](http://latex.artofproblemsolving.com/7/5/9/7596249e635c730943d0f5493ab8e0d9f2399293.png)
.
It is derived through vector geometry.
