Elementary Geometry

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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. Regular hexagon
  3. All interior angles in a regular hexagon are equal to \(120^\circ:\)
    \(\alpha = 120^\circ\)
  4. Apothem of a regular hexagon
    (a perpendicular drawn from the centre to any side)
    \(m = a{\large\frac{{\sqrt 3 }}{2}\normalsize}\)
  5. The radius of the inscribed circle of a regular hexagon is equal to the apothem:
    \(r = m = a{\large\frac{{\sqrt 3 }}{2}\normalsize}\)
  6. The radius of the circumscribed circle of a regular hexagon is equal to the side of the hexagon:
    \(R = a\)
  7. Perimeter of a regular hexagon
    \(P = 6a\)
  8. Area of a regular hexagon
    \(S = pr = {a^2}{\large\frac{{3\sqrt 3 }}{2}\normalsize},\)
    where \(p\) is the semiperimeter of the hexagon.