Octagon
A polygon with eight sides.
Properties
- An octagon is a regular octagon if all its sides are congruent and if all its interior angles have the same measure.
- An octagon has eight interior angles and, if it is a regular octagon, each of its interior angles measures 135°.
- The sum of the interior angles of a convex octagon is 1080°.
Formula
Consider an octagon with a side length c and an apothem a in which r is the radius of the circumscribed circle. A formula to calculate the area A of a regular octagon of radius [latex]r[/latex] is:[latex]A=2r^{2}\sqrt{2}[/latex].
Another formula to calculate the area A of a regular octagon of side length c and apothem a is:[latex]A=4ca[/latex].
The formula to calculate the area A of a regular octagon of side length c is:[latex]A=2c^{2}\left ( 1+\sqrt{2}\right )[/latex].
Exemple
This is a regular octagon inscribed in a circle that has an apothem a: