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:
[latex]A=\frac{3\sqrt{3}}{2}a^{2}[/latex].
- The formula for calculating the radius r of the circle circumscribed about a regular hexagon of side length c is:
[latex]r=c[/latex]
- The formula for calculating the radius r of the circle inscribed in a regular hexagon of side length c is:
[latex]r=\frac{c}{2}\sqrt{3}[/latex]
Examples
This is a regular hexagon:
This is not a regular hexagon:
