# 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.      