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Bretschneider's Formula

Given a general Quadrilateral with sides of lengths $a$, $b$, $c$, and $d$ (Beyer 1987), the Area is given by

A_{\rm quadrilateral} ={\textstyle{1\over 4}}\sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2},

where $p$ and $q$ are the diagonal lengths.

See also Brahmagupta's Formula, Heron's Formula


Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 123, 1987.

© 1996-9 Eric W. Weisstein