Spherical Polygon

A closed geometric figure on the surface of a Sphere which is formed by the Arcs of Great Circles. The spherical polygon is a generalization of the Spherical Triangle. If $\theta$ is the sum of the Radian Angles of a spherical polygon on a Sphere of Radius $r$, then the Area is

$$S=[\theta-(n-2)\pi]r^2.$$

See also Great Circle, Spherical Triangle

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 131, 1987.