Library/Geometry/Plane geometry/Polygons/Arbitrary polygons

Arbitrary polygons

Overview
Important

An arbitrary polygon is a closed plane figure formed by a finite sequence of straight line segments (called sides) connected end to end. The sides may be of any length, and the angles between them may be of any size (greater than 0 and less than 180 degrees for simple polygons). The polygon does not have to be regular or convex.

Important properties

  • The sum of the interior angles of an n-sided polygon is (n−2)×180∘(n-2) \times 180^\circ.

  • Polygons can be classified as convex (all interior angles less than 180°) or concave (at least one interior angle greater than 180°).

  • A simple polygon does not cross itself; a complex polygon may have sides that cross.

  • Arbitrary polygons can have any number of sides n≥3n \geq 3.