# Formulas and Tables

Elementary Geometry# Regular Hexagon

Interior angle: \(\alpha\)

Apothem of a regular hexagon: \(m\)

Area: \(S\)

Radius of the circumscribed circle: \(R\)

Perimeter: \(P\)

Semiperimeter: \(p\)

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

- All interior angles in a regular hexagon are equal to \(120^\circ:\)

\(\alpha = 120^\circ\) - Apothem of a regular hexagon

(a perpendicular drawn from the centre to any side)

\(m = a{\large\frac{{\sqrt 3 }}{2}\normalsize}\) - The radius of the inscribed circle of a regular hexagon is equal to the apothem:

\(r = m = a{\large\frac{{\sqrt 3 }}{2}\normalsize}\) - The radius of the circumscribed circle of a regular hexagon is equal to the side of the hexagon:

\(R = a\) - Perimeter of a regular hexagon

\(P = 6a\) - Area of a regular hexagon

\(S = pr = {a^2}{\large\frac{{3\sqrt 3 }}{2}\normalsize},\)

where \(p\) is the semiperimeter of the hexagon.