Brahmagupta's Formula
For a Quadrilateral with sides of length 
, 
, 
, and 
, the Area 
is given by
 | (1) |
 | (2) |
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 Circleand Circumscribed on another, then the Area Formula simplifies to | (5) |
References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 56-60, 1967. Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 81-82, 1929.
- Fuzzy Logic
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