# Formulas

## Elementary Geometry # Regular Hexagon

Side of a regular hexagon: $$a$$
Interior angle: $$\alpha$$
Apothem of a regular hexagon: $$m$$
Area: $$S$$
Radius of the inscribed circle: $$r$$
Radius of the circumscribed circle: $$R$$
Perimeter: $$P$$
Semiperimeter: $$p$$
1. A regular hexagon is a convex polygon with six equal sides and six equal angles.
2. All interior angles in a regular hexagon are equal to $$120^\circ:$$
$$\alpha = 120^\circ$$
3. Apothem of a regular hexagon
(a perpendicular drawn from the centre to any side)
$$m = a{\large\frac{{\sqrt 3 }}{2}\normalsize}$$
4. The radius of the inscribed circle of a regular hexagon is equal to the apothem:
$$r = m = a{\large\frac{{\sqrt 3 }}{2}\normalsize}$$
5. The radius of the circumscribed circle of a regular hexagon is equal to the side of the hexagon:
$$R = a$$
6. Perimeter of a regular hexagon
$$P = 6a$$
7. Area of a regular hexagon
$$S = pr = {a^2}{\large\frac{{3\sqrt 3 }}{2}\normalsize},$$
where $$p$$ is the semiperimeter of the hexagon.