Irregular Polygon Definition - Math Open Reference

Irregular Polygon

Definition: Any polygon that is not a regular polygon. A polygon whose sides are not all the same length or whose interior angles do not all have the same measure.

(See also Regular Polygon)

Try this Adjust the polygon below by dragging any orange dot. Note that only the vertex you drag is affected.

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An irregular polygon is any polygon that is not a regular polygon. It can have sides of any length and each interior angle can be any measure. They can be convex or concave, but all concave polygons are irregular since the interior angles cannot all be the same. If you drew a polygon at random, it would probably be irregular.

Specific irregular polygons such as a parallelogram have some interesting properties and have their own web pages.

Equilateral Polygons

Equilateral means that all sides are the same length. But as can be seen from the figure below, this can still be irregular. This figure has all sides the same length, but it does not have all angles the same, so it is irregular. A polygon with six equal sides, but with one vertex pushed inwards. making it concave

A polygon with six equal sides, but with one vertex pushed inwards. making it concave

Attributes

Vertex	The vertex (plural: vertices) is a corner of the polygon. In any polygon, the number of sides and vertices are always equal.
Side	The sides are the straight line segments that make up the polygon.
Area	There is no easy formula for the area of an irregular polygon, but see Area of a Irregular Polygon for some general approaches to the problem.
Perimeter	The sum of the lengths of the sides. See Perimeter of a polygon

Equilateral Polygons

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons