# Hexagon

A hexagon is a polygon with six sides and six vertices.

## Regular Hexagons

A regular hexagon is a polygon with six equal sides and angles.

The triangles formed by joining the center with all the vertices are equal in size and are equilateral.

#### Angles of the Hexagon

The sum of interior angles of a hexagon = (6 − 2) · 180° = **720°**

The value of an interior angle of the regular hexagon is 720º : 6 = **120º**

The central angle of the regular hexagon measures: 360º : 6 = **60º**

#### Diagonals of the Hexagon

The number of diagonals = 6 · (6 − 3) : 2 = **9**

#### Apothem of a Regular Hexagon

By applying the Pythagorean theorem for one of the triangles, we obtain:

#### Perimeter of a Regular Hexagon

**Perimeter = 6 · l**

#### Area of a Regular Hexagon

#### Examples

Calculate the apothem, perimeter and area of a regular hexagon inscribed in a circle with a radius of 4 cm.

P = 6 · 4 = **24 cm**

The area of a square is 2,304 cm². Calculate the area of a regular hexagon that has the same perimeter as this square.