Bretschneider's formula

He is best known for his discovery of Bretschneider's formula.

It is a corollary to Bretschneider's formula since opposite angles are supplementary.

This more general formula is known as Bretschneider's formula.

Bretschneider's formula expresses the area in terms of the sides and two opposite angles:

Bretschneider's formula works on any convex quadrilateral, whether it is cyclic or not.

The formula is also a special case of Bretschneider's formula for a general quadrilateral).

This is another corollary to Bretschneider's formula.

In geometry, Bretschneider's formula is the following expression for the area of a general convex quadrilateral:

Bretschneider's formula generalizes this to all quadrilaterals:

Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral.

Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the quadrilateral to zero.

Note that this is the same formula as the one for the area of a tangential quadrilateral and it is also derived from Bretschneider's formula in the same way.

Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.