A four-sided Polygon sometimes (but not very often) also known as a Tetragon. If not explicitly stated, all four Vertices are generally taken to lie in a Plane. If the points do not lie in a Plane, the quadrilateral is called a Skew Quadrilateral.

For a planar convex quadrilateral (left figure above), let the lengths of the sides be , , , and , the
Semiperimeter , and the Diagonals and . The Diagonals are Perpendicular Iff
. An equation for the sum of the squares of side lengths is

(1) |

(2) | |||

(3) | |||

(4) | |||

(5) |

where (4) is known as Bretschneider's Formula (Beyer 1987).

A special type of quadrilateral is the Cyclic Quadrilateral, for which a Circle can be circumscribed so that it
touches each Vertex. For Bicentric quadrilaterals, the
Circumcircle and Incircle satisfy

(6) |

There is a relationship between the six distances , , , , , and between the four points of a quadrilateral (Weinberg 1972):

(7) |

**References**

Beyer, W. H. (Ed.) *CRC Standard Mathematical Tables, 28th ed.* Boca Raton, FL: CRC Press, p. 123, 1987.

Routh, E. J. ``Moment of Inertia of a Quadrilateral.'' *Quart. J. Pure Appl. Math.* **11**, 109-110, 1871.

Weinberg, S. *Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity.*
New York: Wiley, p. 7, 1972.

© 1996-9

1999-05-25