In geometry, Bretschneider's formula is a mathematical expression for the area of a general quadrilateral, and it works for both convex and concave quadrilaterals whether or not they are cyclic.
Facts
StatementThe area K of a general quadrilateral with sides a, b, c and d, semiperimeter s, and opposite angles alpha and gamma equals the square root of the quantity (s-a)(s-b)(s-c)(s-d) minus abcd times the square of the cosine of half the sum of alpha and gamma. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Source Bretschneider's formula, Wikipedia
Sources
1. Bretschneider's formula, Wikipedia
Formulation section
Bretschneider's formula is expressed as: K = sqrt[(s-a)(s-b)(s-c)(s-d) - abcd*cos^2((alpha+gamma)/2)]
History section
The German mathematician Carl Anton Bretschneider discovered the formula in 1842.
In Branch: Geometry, Lead sentence
In geometry, Bretschneider's formula is a mathematical expression for the area of a general quadrilateral.
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