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 16:41, 21 June 2006
Let us have a quadrilateral with side lengths , and diagonals . Bretschneider's formula says that . It is derived through vector geometry.