This article is about four-sided mathematical shapes. For other uses, see Quadrilateral (disambiguation).
"Tetragon" redirects here. For the edible plant, see Tetragonia tetragonioides.
Quadrilateral
Some types of quadrilaterals
Edges and vertices
4
Schläfli symbol
{4} (for square)
Area
various methods; see below
Internal angle (degrees)
90° (for square and rectangle)
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]
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]
^"Sum of Angles in a Polygon". Cuemath. Retrieved 22 June 2022.
^Martin, George Edward (1982), Transformation geometry, Undergraduate Texts in Mathematics, Springer-Verlag, Theorem 12.1, page 120, doi:10.1007/978-1-4612-5680-9, ISBN 0-387-90636-3, MR 0718119
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