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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