# Types of Polygons

By the end of this lesson, you will be able to

- define polygon.
- classify different types of polygons.
- describe regular polygon and irregular polygon.
- analyze why polygon is a generalization of all triangles and quadrilaterals.
- interpret simple polygon and complex polygon.
- explain self-intersecting polygon.
- demonstrate examples of polygon.

## Polygon

A polygon is a plane closed shape formed by connecting a number of coplanar line segments.

The line segments, each connected to end to end are called the sides or edges of the polygon. The points where each pair of adjacent sides or edges meet are called the vertices or corners of the polygon. A polygon with n sides is known as n-gon.

A triangle is the least polygon in terms of number of sides and it is a 3-gon. Consequently, a quadrilateral is a 4-gon and a pentagon is a 5-gon.

### Polygon Example

## Classification of Polygons

Polygons are generally divided into two parts with respect to self-intersecting:

- Simple polygon (none self-intersecting)
- Complex polygon (self-intersecting)

### Simple Polygon

A polygon is said to be a simple polygon if it is not self-intersecting.

Simple polygons are comprised of convex and concave polygon; that is simple polygons are divided into two parts:

- Convex polygon
- Concave polygon

### Convex Polygon

A convex polygon is a polygon in which all interior angles are less than 180°.

All the diagonals lie entirely inside the polygon. All corners or vertices approach to outward away from interior of the polygon. Any straight line, except tangent at vetex, passing through the convex polygon intersects exactly twice to its boundary. Again, any line segment connected to its endpoints on its boundary lie entirely inside the polygon.

All interior angles of this polygon are less than 180°.

### Concave Polygon

One interior angles is less than 180°

A concave polygon is a polygon in which at least one interior angles is greater than 180^{0}.

At least one vertex pushed in

towards the interior of the polygon. Any straight line passing through the concave polygon intersects more than twice to its boundary. Some of the diagonals of a concave polygon may lie outside the polygon.

### Complex Polygon

A complex polygon is a polygon if it is self-intersecting. For a complex polygon, two sides intersect at the different common point on the sides except vertex.

### Star Polygon

A non-convex polygon is called a star polygon. This implies that every concave polygon is also a star polygon.

There are two types of star polygons are discussed in mathematics.

- Regular star polygon
- Irregular star polygon or isotoxal star polygon

### Regular Star Polygon

A self-intersecting polygon is called a regular star polygon if it is a both equilateral and equiangular.

Equilateral means that all sides or edges of the polygon are equal in length.

And equiangular indicates that all interior angles of the polygon are equal to each other.

A regular star polygon is showing its equal sides and equal angles.

### Irregular Star Polygon

One interior angles is less than 180°

An irregular star polygon or isotoxal star polygon is one of the concave polygons. This type of polygon is produced by removing the intersecting lines inside from a regular star polygon. For an isotoxal star polygon, no lines are self intersecting and all angles are not equal. So it can never be regular star polygon.

Equilateral means that all sides or edges of the polygon are equal in length.

### Regular Polygon

A regular convex polygon is a simple polygon in which all sides are equal in length and all interior angles are equal in measure.

As all sides are equal for a regular convex polygon, its angles are also equal.

A regular polygon

### Irregular Polygon

An irregular polygon

An irregular convex polygon is a simple polygon in which all sides are not equal in lngth. As a result, all angles are also not equal in measure for an irregular polygon.