# Hendecagons - polygons with 11 sides

Categories: gcse geometry

A hendecagon is a flat shape with 11 straight sides.

## Regular and irregular hendecagons

A *regular hendecagon* is a 11-sided shape where every side is the same length and every corner has the same angle. All regular hendecagons have the same shape, like this:

An *irregular hendecagon* is a 11 sides shape where not every side and angle are equal. There are many different irregular hendecagon shapes, here is an example:

## Name

The name *hendecagon* is a combination of the words *hendeca* (Greek meaning *eleven*) and *gonia* (Greek meaning *corner*).

Hendecagons are sometimes called *11-gons*.

## Interior angles

The interior angles of a hendecagon are shown here:

The sum of these 11 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 11, so the sum of the interior angles is:

```
(11 - 2) x 180 = 1620 degrees
```

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

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

```
1620 / 11 = 147.27 degrees (approximately)
```

## Exterior angles

The exterior angles of a hendecagon are shown here:

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

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

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

```
360 / 11 = 32.73 degrees (approximately)
```

## Symmetry of regular hendecagons

A regular hendecagon has 11 lines of symmetry. This means that it can be reflected over each of the 11 grey lines shown here:

A regular hendecagon has rotational symmetry of order 11. This means that if it rotated about its centre by a 11th of a full turn, it will map onto itself:

## Real life examples

The Canadian 1 dollar coin is based on the regular hendecagon.

## 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
- Nonagons - polygons with 9 sides
- Decagons - polygons with 10 sides
- Dodecagons - polygons with 12 sides
- n-gons - polygons with any number of sides
- Other types of polygon
- Star polygons

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