# Quadrilateral

In geometry a **quadrilateral** is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words *quadri*, a variant of four, and *latus*, meaning "side". It is also called a **tetragon**, derived from greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon). Since "gon" means "angle", it is analogously called a **quadrangle**, or 4-angle. A quadrilateral with vertices , , and is sometimes denoted as .[1]

Quadrilateral | |
---|---|

Edges and vertices | 4 |

Schläfli symbol | {4} (for square) |

Area | various methods; see below |

Internal angle (degrees) | 90° (for square and rectangle) |

Quadrilaterals are either simple (not self-intersecting), or complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave.

The interior angles of a simple (and planar) quadrilateral *ABCD* add up to 360 degrees of arc, that is[1]

This is a special case of the *n*-gon interior angle sum formula: *S* = (*n* − 2) × 180°.[2]

All non-self-crossing quadrilaterals tile the plane, by repeated rotation around the midpoints of their edges.[3]