Hexagon

Hexagon

Polygon with six sides.

Properties

  • A hexagon is a regular hexagon if all its sides are congruent and if all its interior angles are congruent.
  • Each of the interior angles of a regular hexagon measures 120°.
    Therefore, the sum of its interior angles is 720°.
  • A plane can be tessellated with regular hexagons.
  • A regular hexagon has 6 axes of symmetry; 3 axes of symmetry pass through the opposite vertices and the centre (the solid lines in the figure below) and 3 axes of symmetry pass through the midpoints of the opposite sides and the centre (the dashed lines in the figure below).

Formulas

  • The area of a regular hexagon of side length a is given by:

\(A=\frac{3\sqrt{3}}{2}a^{2}\).

  • The formula for calculating the radius r of the circle circumscribed about a regular hexagon of side length c is:

\(r=c\)

  • The formula for calculating the radius r of the circle inscribed in a regular hexagon of side length c is:

\(r=\frac{c}{2}\sqrt{3}\)

Examples

This is a regular hexagon:

This is not a regular hexagon:

Historical note

During the 17th century, the Sicilian cities of Avola and Grammichele, which had been destroyed by an earthquake in 1693, were rebuilt using a hexagonal plan, following an example of Renaissance architectural ideals.

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