Bretschneider's formula
From AoPSWiki
Suppose we have a quadrilateral with edges 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://alt2.artofproblemsolving.com/Forum/latexrender/pictures/9/0/f/90fad195033a211ac680ae3830585805d63502cb.gif "Click on the formula to view the LaTeX code")
.
It can be derived with vector geometry.
Proof
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See Also
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