## Brahmagupta's Formula

For a Quadrilateral with sides of length , , , and , the Area is given by

 (1)

where
 (2)

is the Semiperimeter, is the Angle between and , and is the Angle between and . For a Cyclic Quadrilateral (i.e., a Quadrilateral inscribed in a Circle), , so
 (3) (4)

where is the Radius of the Circumcircle. If the Quadrilateral is Inscribed in one Circle and Circumscribed on another, then the Area Formula simplifies to
 (5)