Polygon with six sides.

### Properties

- A hexagon is a regular hexagon if all its sides are congruent and if all its interior angles are congruent.
- Each of the interior angles of a regular hexagon measures 120°.

Therefore, the sum of its interior angles is 720°. - A plane can be tessellated with regular hexagons.
- A regular hexagon has 6 axes of symmetry; 3 axes of symmetry pass through the opposite vertices and the centre (
*the solid lines in the figure below*) and 3 axes of symmetry pass through the midpoints of the opposite sides and the centre (*the dashed lines in the figure below*).

### Formulas

- The area of a regular hexagon of side length
*a*is given by:

\(A=\frac{3\sqrt{3}}{2}a^{2}\).

- The formula for calculating the radius
*r*of the circle circumscribed about a regular hexagon of side length*c*is:

\(r=c\)

- The formula for calculating the radius
*r*of the circle inscribed in a regular hexagon of side length c is:

\(r=\frac{c}{2}\sqrt{3}\)

### Examples

This is a regular hexagon:

This is not a regular hexagon:

### Historical note

During the 17th century, the Sicilian cities of Avola and Grammichele, which had been destroyed by an earthquake in 1693, were rebuilt using a hexagonal plan, following an example of Renaissance architectural ideals.