# 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

 Number of vertices (n): Side length (b): Pi: Pi3.1422/7355/113

## 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.