Hexagons - polygons with 6 sides
Categories: gcse geometry
A hexagon is a flat shape with 6 straight sides.
Regular and irregular hexagons
A regular hexagon is a 6-sided shape where every side is the same length and every corner has the same angle. All regular hexagons have the same shape, like this:
An irregular hexagon is a 6 sides shape where not every side and angle are equal. There are many different irregular hexagon shapes, here is an example:
Name
The name hexagon is a combination of the words hex (Greek meaning six) and gonia (Greek meaning corner).
Hexagons are sometimes called 6-gons.
Interior angles
The interior angles of a hexagon are shown here:
The sum of these 6 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 6, so the sum of the interior angles is:
(6 - 2) x 180 = 720 degrees
For a regular hexagon, all the interior angles are equal:
This means that the interior angle of a regular hexagon is:
720 / 6 = 120 degrees
Exterior angles
The exterior angles of a hexagon are shown here:
The sum of the exterior angles of any polygon is 360 degrees.
For a regular hexagon, all the interior angles are equal:
This means that the exterior angle of a regular hexagon is:
360 / 6 = 60 degrees
Symmetry of regular hexagons
A regular hexagon has 6 lines of symmetry. This means that it can be reflected over each of the 6 grey lines shown here:
A regular hexagon has rotational symmetry of order 6. This means that if it rotated about its centre by a 6th of a full turn, it will map onto itself:
Real life examples
Regular hexagons tessellate, so it is a popular shape for floor tiles. The only other regular polygons that tessellate are squares and equilateral triangles.
See also
- Regular polygons
- Interior and exterior angles of a polygon
- Triangles
- Quadrilaterals
- Quadrilateral family tree
- Pentagons - polygons with 5 sides
- Heptagons - polygons with 7 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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