Articles containing proofs | Area | Theorems about quadrilaterals

Bretschneider's formula

In geometry, Bretschneider's formula is the following expression for the area of a general quadrilateral: Here, a, b, c, d are the sides of the quadrilateral, s is the semiperimeter, and α and γ are any two opposite angles, since as long as Bretschneider's formula works on both convex and concave quadrilaterals (but not crossed ones), whether it is cyclic or not. The German mathematician Carl Anton Bretschneider discovered the formula in 1842. The formula was also derived in the same year by the German mathematician Karl Georg Christian von Staudt. (Wikipedia).

Bretschneider's formula
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Related pages

Cyclic quadrilateral | Brahmagupta's formula | Carl Anton Bretschneider | Karl Georg Christian von Staudt | Area | Law of cosines | Heron's formula | Geometry | Triangle | Quadrilateral | Semiperimeter