# Polygon

A polygon is a shape of plane geometry. It’s made of straight lines connected to each other forming a “closed” shape.

Polygon comes from the Greek words ”poly”, meaning “many”, and “gonia”, meaning "angles". So it’s a shape with many angles.

## Types of polygons

There are several types of polygons.

Here are the most typical of them:

Convex | Concave |

All angles are less than 180˚ | One or more angles are more than 180˚. |

Regular | Irregular |

All angles and sides are equal. | Not all angles and sides are equal. |

## Convex polygons

**Angle sum**

The angle sum of a convex polygon with n sides is given by:

Triangles and rectangles are typical examples of convex polygons.

Let’s try to calculate the angle sum of the these two shapes with the formula above:

Triangle:

Rectangle:

## Regular polygons

Regular polygons are the only polygons of which it’s possible to make general formulas applicable to all of them.**The circumference of a regular polygon**

where C is the circumference, n is the number of sides, and b is the side length.**The area of a regular polygon**

Where A is the area, n is the number of sides, and b is the side length.

Use the following formula instead, if your calculator hasn't got the cotangent feature.

## Area and circumference of a regular polygon

## Names of polygons

A polygon is named after its number of vertices.

Name | meaning | Angle sum | Examples |

Trigon | Triangle | 180 | The triangle is an important shape in triangulation. Triangulation was used in the old days to determine locations and to create maps. |

Tetragon | Quadrilateral | 360 | A football field |

Pentagon | 5-sided shape | 540 | The headquarters of the United States Department of Defense |

Hexagon | 6-sided shape | 720 | The hexagon is common in nature and in chemistry, for example the pattern you see inside a beehive or the structure of sugar molecules. |

Heptagon or septagon | 7-sided shape | 900 | British coins: 20 and 50 pence. |

Octagon | 8-sided shape | 1080 | Stop sign in traffic. |