Brahmagupta's Formula

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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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