Hexagons - polygons with 6 sides

By Martin McBride, 2022-10-10
Tags: hexagon 6 sided shape regular polygon irregular polygon
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:

Regular hexagon

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:

Irregular hexagon


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:

Interior angles of a hexagon

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:

Interior angles of an irregular hexagon

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:

Exterior angles of a hexagon

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

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

Exterior angles of an irregular hexagon

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:

Lines of symmetry of a regular nonangon

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:

Lines of symmetry of a regular hexagon

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

Join the GraphicMaths Newletter

Sign up using this form to receive an email when new content is added:

Popular tags

adder adjacency matrix alu and gate angle area argand diagram binary maths cartesian equation chain rule chord circle cofactor combinations complex polygon complex power complex root cosh cosine cosine rule cpu cube decagon demorgans law derivative determinant diagonal directrix dodecagon ellipse equilateral triangle eulers formula exponent exponential exterior angle first principles flip-flop focus gabriels horn gradient graph hendecagon heptagon hexagon horizontal hyperbola hyperbolic function infinity integration by substitution interior angle inverse hyperbolic function inverse matrix irregular polygon isosceles trapezium isosceles triangle kite koch curve l system locus maclaurin series major axis matrix matrix algebra minor axis nand gate newton raphson method nonagon nor gate normal not gate octagon or gate parabola parallelogram parametric equation pentagon perimeter permutations polar coordinates polynomial power probability probability distribution product rule pythagoras proof quadrilateral radians radius rectangle regular polygon rhombus root set set-reset flip-flop sine sine rule sinh sloping lines solving equations solving triangles square standard curves star polygon straight line graphs surface of revolution symmetry tangent tanh transformations trapezium triangle turtle graphics vertical volume of revolution xnor gate xor gate