# Hexagon

## Hexagon

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.