Quadrilateral

Quadrilateral
Some types of quadrilaterals
Edges and vertices	4
Schläfli symbol	{4} (for square)
Area	various methods, usually base time height
Internal angle (degrees)	90° (for square and rectangle)

A quadrilateral

In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices (or corners). Sometimes, a quadrilateral is called a quadrangle (similar to the term "triangle"), while other times, the term tetragon is used (similar to other polygon names such as pentagon and hexagon). The origin of the word quadrilateral is the two Latin words quadri, a variant of four, and latus, meaning "side".

A quadrilateral with vertices $A$, $B$, $C$, $D$ is sometimes written as $\square ABCD$.

All the sides of a quadrilateral are straight, and the interior angles of a quadrilateral add up to 360°.

$\angle A+\angle B+\angle C+\angle D=360^{\circ }.$

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

Almost all quadrilaterals tile the plane, by repeated rotation around the midpoints of their edges. The only quadrilaterals that do not do this are the ones with edges that intersect with each other.

Kinds of quadrilaterals

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

There are different kinds of simple quadrilaterals. A trapezoid is a quadrilateral with one pair of parallel edges, where one edge is shorter than the other. A parallelogram is a quadrilateral with two pairs of parallel edges.

Squares, rectangles, and rhombuses are special types of parallelograms. A rectangle has four right angles, while a rhombus has four sides of the same length. A square has four right angles and four sides of the same length, making it a regular polygon. This makes squares a type of rectangle and rhombus.

Related pages

• Cube
• Cuboid