# Heptagons - polygons with 7 sides

Categories: gcse geometry

A heptagon is a flat shape with 7 straight sides.

## Regular and irregular heptagons

A *regular heptagon* is a 7-sided shape where every side is the same length and every corner has the same angle. All regular heptagons have the same shape, like this:

An *irregular heptagon* is a 7 sides shape where not every side and angle are equal. There are many different irregular heptagon shapes, here is an example:

## Name

The name *heptagon* is a combination of the words *hepta* (derived from the Greek for *seven*) and *gonia* (Greek meaning *corner*).

Heptagons are sometimes called Septagons based on the Latin word *septua* (meaning *seven*).

Heptagons are sometimes called *7-gons*.

## Interior angles

The interior angles of a heptagon are shown here:

The sum of these 7 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 7, so the sum of the interior angles is:

```
(7 - 2) x 180 = 900 degrees
```

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

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

```
900 / 7 = 128.57 degrees (approximately)
```

## Exterior angles

The exterior angles of a heptagon are shown here:

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

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

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

```
360 / 7 = 51.43 degrees (approximately)
```

## Symmetry of regular heptagons

A regular heptagon has 7 lines of symmetry. This means that it can be reflected over each of the 7 grey lines shown here:

A regular heptagon has rotational symmetry of order 7. This means that if it rotated about its centre by a 7th of a full turn, it will map onto itself:

## Real-life examples

Some coins are regular heptagons, for example, British 20p and 50p coins.

Many US police badges have a heptogram shape (a heptogram is a str based on the points of a heptogon).

## 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
- 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

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