# Regular polygons

Categories: gcse geometry

A regular polygon is a polygon for which every side is equal and every angle is equal. In this section we will look at some well known regular polygons with 3 to 12 sides. Here is a video:

## Interior and exterior angles of regular polyons

This section gives the formulas for the interior and exterior angles of a polygon.

For a regular polygon, we know that all the interior angles are equal, and also that all the exterior angles are equal. We can use this to show that. for a regular polygon of *n* sides:

$$ exterior = \frac{360°}{n} $$

$$ interior = 180° - \frac{360°}{n} $$

## 3 sides - equilateral triangle

A three sided shape, of course, is called a triangle. A regular triangle is called an equilateral triangle, and looks like this:

Interior angle of a equilateral triangle is 60.0°

Exterior angle of a equilateral triangle is 120.0°

## 4 sides - square

A four sided shape is called a quadrilateral. A regular quadrilaterals are more commonly known as squares:

Interior angle of a square is 90.0°

Exterior angle of a square is 90.0°

## 5 sides - pentagon

A five sided shape is called a pentagon. A regular pentagon looks like this:

Interior angle of a regular pentagon is 108.0°

Exterior angle of a regular pentagon is 72.0°

## 6 sides - hexagon

A six sided shape is called a hexagon. A regular hexagon looks like this:

Interior angle of a regular hexagon is 120.0°

Exterior angle of a regular hexagon is 60.0°

## 7 sides - heptagon

A seven sided shape is called a heptagon. A regular heptagon looks like this:

Interior angle of a regular heptagon is 128.57°

Exterior angle of a regular heptagon is 51.43°

## 8 sides - octagon

A eight sided shape is called an octagon. A regular octagon looks like this:

Interior angle of a regular octagon is 135.0°

Exterior angle of a regular octagon is 45.0°

## 9 sides - nonagon

A nine sided shape is called a nonagon. A regular nonagon looks like this:

Interior angle of a regular nonagon is 140.0°

Exterior angle of a regular nonagon is 40.0°

## 10 sides - decagon

A ten sided shape is called a decagon. A regular decagon looks like this:

Interior angle of a regular decagon is 144.0°

Exterior angle of a regular decagon is 36.0°

## 11 sides - hendecagon

An eleven sided shape is called a hendecagon. A regular hendecagon looks like this:

Interior angle of a regular hendecagon is 147.27°

Exterior angle of a regular hendecagon is 32.73°

## 12 sides - dodecagon

A twelve sided shape is called a dodecagon. A regular dodecagon looks like this:

Interior angle of a regular dodecagon is 150.0°

Exterior angle of a regular dodecagon is 30.0°

## Polygons with more sides

A polygon can have any number of sides, but most do not have well known special names.

## Irregular polygons

An irregular polygon is a polygon where some of the sides and/or angles are different. Some irregular triangles and quadrilaterals have special names (isosceles triangle, rectangle, parallelogram, etc), but irregular shapes with more than four side usually don't.

## See also

- Interior and exterior angles of a polygon
- Triangles
- Quadrilaterals
- Quadrilateral family tree
- Pentagons - polygons with 5 sides
- Hexagons - polygons with 6 sides
- Heptagons - polygons with 7 sides
- Octagons - polygons with 8 sides
- Nonagons - polygons with 9 sides
- Decagons - polygons with 10 sides
- Hendecagons - polygons with 11 sides
- Dodecagons - polygons with 12 sides
- n-gons - polygons with any number of sides
- Other types of polygon
- Star polygons

## Join the GraphicMaths Newletter

Sign up using this form to receive an email when new content is added:

## Popular tags

angle area cartesian equation chord circle combinations complex polygon cosh cosine cosine rule cube decagon derivative diagonal directrix dodecagon ellipse equilateral triangle exponent exponential exterior angle focus gradient hendecagon heptagon hexagon horizontal hyperbola hyperbolic function interior angle inverse hyperbolic function irregular polygon isosceles trapezium isosceles triangle kite locus major axis minor axis newton raphson method nonagon normal octagon parabola parallelogram parametric equation pentagon perimeter permutations power pythagoras proof quadrilateral radius rectangle regular polygon rhombus root sine sine rule sinh sloping lines solving equations solving triangles square standard curves star polygon straight line graphs symmetry tangent tanh transformations trapezium triangle vertical