If a cyclic quadrilateral ABCD has
sides of lengths a, b, c, and d, and the semiperimeter
, then
the area is given by:
Brahmagupta (598–668) was an Indian
mathematician and astronomer. See also:
Brahmagupta's Theorem.
Heron's formula is a special case of this formula, when one of
the sides equal zero. The relationship between the general Brahmagupta's formula and the Heron's formula is similar to how
the law of cosines extends the Pythagorean theorem.
