GraphicMaths - Octagons - polygons with 8 sides (2024)

A octagon is a flat shape with 8 straight sides.

Regular and irregular octagons

A regular octagon is a 8-sided shape where every side is the same length and every corner has the same angle. All regular octagons have the same shape, like this:

An irregular octagon is a 8 sides shape where not every side and angle are equal. There are many different irregular octagon shapes, here is an example:

Name

The name octagon is from the Greek octagonon (meaning octagon).

Octagons are sometimes called 8-gons.

Interior angles

The interior angles of a octagon are shown here:

The sum of these 8 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 8, so the sum of the interior angles is:

(8 - 2) x 180 = 1080 degrees

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

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

1080 / 8 = 135 degrees

Exterior angles

The exterior angles of a octagon are shown here:

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

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

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

360 / 8 = 45 degrees

Symmetry of regular octagons

A regular octagon has 8 lines of symmetry. This means that it can be reflected over each of the 8 grey lines shown here:

A regular octagon has rotational symmetry of order 8. This means that if it rotated about its centre by a 8th of a full turn, it will map onto itself:

Real life examples

Octagons are common design elements: signs (traffic Stop signs are octagonal in many countries), floor tiles, biscuit tins, even quirky window frames. This is partly because the angles in a regular octagon are all multiples of 45 degrees which often makes items of that shape easier to manufacture.

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
• 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