# Nonagons - polygons with 9 sides

Categories: gcse geometry

A nonagon is a flat shape with 9 straight sides.

## Regular and irregular nonagons

A *regular nonagon* is a 9-sided shape where every side is the same length and every corner has the same angle. All regular nonagons have the same shape, like this:

An *irregular nonagon* is a 9 sides shape where not every side and angle are equal. There are many different irregular nonagon shapes, here is an example:

## Name

The name *nonagon* is a combination of the words *nonus* (Latin meaning *ninth*) and *gonon* (Latin meaning *angle* or *corner*).

This is slightly unusual because most polygons use greek numbers in their name. An alternative name for a nonagon is *enneagon*, based on the Greek word *ennea* (meaning nine). This name isn't used very often.

Nonagons are sometimes called *9-gons*.

## Interior angles

The interior angles of a nonagon are shown here:

The sum of these 9 angles is given by the formula:

```
sum of interior angles = (n - 2) x 180
```

Where *n* is the number of sides. In this case, the number of sides *n* is 9, so the sum of the interior angles is:

```
(9 - 2) x 180 = 1260 degrees
```

For a regular nonagon, all the interior angles are equal:

This means that the interior angle of a regular nonagon is:

```
1260 / 9 = 140 degrees
```

## Exterior angles

The exterior angles of a nonagon are shown here:

The sum of the exterior angles of *any polygon* is 360 degrees.

For a regular nonagon, all the interior angles are equal:

This means that the exterior angle of a regular nonagon is:

```
360 / 9 = 40 degrees
```

## Symmetry of regular nonagons

A regular nonagon has 9 lines of symmetry. This means that it can be reflected over each of the 9 grey lines shown here:

A regular nonagon has rotational symmetry of order 9. This means that if it rotated about its centre by a 9th of a full turn, it will map onto itself:

## See also

- Regular polygons
- 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
- 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

adder adjacency matrix alu and gate angle area argand diagram binary maths cartesian equation chain rule chord circle cofactor combinations complex modulus complex polygon complex power complex root cosh cosine cosine rule cpu cube decagon demorgans law derivative determinant diagonal directrix dodecagon eigenvalue eigenvector ellipse equilateral triangle euler eulers formula exponent exponential exterior angle first principles flip-flop focus gabriels horn gradient graph hendecagon heptagon hexagon horizontal hyperbola hyperbolic function hyperbolic functions infinity integration by parts integration by substitution interior angle inverse hyperbolic function inverse matrix irrational irregular polygon isosceles trapezium isosceles triangle kite koch curve l system line integral locus maclaurin series major axis matrix matrix algebra mean minor axis nand gate newton raphson method nonagon nor gate normal normal distribution not gate octagon or gate parabola parallelogram parametric equation pentagon perimeter permutations polar coordinates polynomial power probability probability distribution product rule proof pythagoras proof quadrilateral radians radius rectangle regular polygon rhombus root set set-reset flip-flop sine sine rule sinh sloping lines solving equations solving triangles square standard curves standard deviation star polygon statistics straight line graphs surface of revolution symmetry tangent tanh transformation transformations trapezium triangle turtle graphics variance vertical volume of revolution xnor gate xor gate