Decagons - polygons with 10 sides
Categories: gcse geometry
A decagon is a flat shape with 10 straight sides.
Regular and irregular decagons
A regular decagon is a 10-sided shape where every side is the same length and every corner has the same angle. All regular decagons have the same shape, like this:
An irregular decagon is a 10 sides shape where not every side and angle are equal. There are many different irregular decagon shapes, here is an example:
Name
The name decagon is a combination of the words deca (Greek meaning five) and gonia (Greek meaning corner).
Decagons are sometimes called 10-gons.
Interior angles
The interior angles of a decagon are shown here:
The sum of these 10 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 10, so the sum of the interior angles is:
(10 - 2) x 180 = 1440 degrees
For a regular decagon, all the interior angles are equal:
This means that the interior angle of a regular decagon is:
1440 / 10 = 144 degrees
Exterior angles
The exterior angles of a decagon are shown here:
The sum of the exterior angles of any polygon is 360 degrees.
For a regular decagon, all the interior angles are equal:
This means that the exterior angle of a regular decagon is:
360 / 10 = 36 degrees
Symmetry of regular decagons
A regular decagon has 10 lines of symmetry. This means that it can be reflected over each of the 10 grey lines shown here:
A regular decagon has rotational symmetry of order 10. This means that if it rotated about its centre by a 10th 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
- Nonagons - polygons with 9 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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