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 \(r\) is:

\(A=2r^{2}\sqrt{2}\).

Another formula to calculate the area *A* of a regular octagon of side length *c* and apothem *a* is:

\(A=4ca\).

The formula to calculate the area *A* of a regular octagon of side length *c* is:

\(A=2c^{2}\left ( 1+\sqrt{2}\right )\).

### Exemple

This is a regular octagon inscribed in a circle that has an apothem *a*: