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
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Suppose we have a [[quadrilateral]] with sides of length <math>a,b,c,d</math> and diagonals of length <math>p, q</math>. '''Bretschneider's formula''' states 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.
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It can be derived with [[vector]] geometry.

Revision as of 22:06, 30 June 2006

Suppose we have a quadrilateral with sides of length $a,b,c,d$ and diagonals of length $p, q$. Bretschneider's formula states that $[ABCD]=\frac{1}{4}*\sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2}$.

It can be derived with vector geometry.