Brahmagupta's Formula
Brahmagupta's formula is a formula for determining the area of a cyclic quadrilateral given only the four side lengths.
Definition
Given a cyclic quadrilateral has side lengths , the area can be found as:
where the semiperimeter .
Similar formulas
Bretschneider's formula gives a formula for the area of a non-cyclic quadrilateral given only the side lengths; applying Ptolemy's Theorem to Bretschneider's formula reduces it to Brahmagupta's formula.
Brahmagupta's formula reduces to Heron's formula by setting the side length .
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