Quadrilateral
Polygon with four sides and four corners / From Wikipedia, the free encyclopedia
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]
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \angle A+\angle B+\angle C+\angle D=360^{\circ}.}
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]