Octagons - polygons with 8 sides
Categories: gcse geometry
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
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