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.