Brahmagupta's formula

Brahmagupta's formula gives the area of a cyclic quadrilateral from its side lengths: the square root of the product of the semiperimeter minus each side.

Ptolemy's theorem: For a cyclic quadrilateral, the product of its diagonals equals the sum of the products of opposite sides. Its relation among sides and diagonals helps derive the area formula.
Quadrilateral: A polygon with four sides and four vertices. The formula concerns the area of this four-sided figure.
Brahmagupta: An Indian mathematician and astronomer who lived from 598 to after 665. The formula bears the name of the mathematician who stated it in his treatise.
Surveying: The practice of measuring and mapping land and other physical spaces. Measured side lengths can determine area when the surveyed quadrilateral is cyclic.
Bretschneider's formula: A formula for a quadrilateral's area from its side lengths and two opposite angles. It gives the general area relation from which Brahmagupta's cyclic case follows.
Circle: The set of points in a plane at a fixed distance from a center. A cyclic quadrilateral is defined by its vertices lying on one circle.
Brahmasphutasiddhanta: A Sanskrit treatise on mathematics and astronomy completed by Brahmagupta in 628. Brahmagupta presented the quadrilateral area rule in this work.
Land surveying: Surveying focused on measuring and mapping land boundaries and features. A cyclic boundary permits area calculation from four measured sides alone.
Semiperimeter: Half the perimeter of a polygon. The formula combines the semiperimeter with each side length.
Area: A measure of the two-dimensional extent of a region. The formula calculates this quantity for a cyclic quadrilateral.

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