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

References

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