Because an octagon has an even number of sides, in a regular octagon, opposite sides are parallel.
| Interior angle | 135° | Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For an octagon, n=8. See Interior Angles of a Polygon |
| Exterior Angle | 45° | To find the exterior angle of a regular octagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon |
| Area | 4.828s2 approx | Where S is the length of a side. To find the exact area of an octagon or any polygon, using various methods, see Area of a Regular Polygon and Area of an Irregular Polygon |
| Number of diagonals | 20 | The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon |
| Number of triangles | 6 | The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon |
| Sum of interior angles | 1080° | In general 180(n–2) degrees . See Interior Angles of a Polygon |
Houses and rooms are sometimes built in an octagonal shape (pronounced: "ock-TAG-on-all"), perhaps because they feel somewhat like a circular space but are made of straight wall sections which are easier to build.
While no longer so popular, there are examples that are being preserved as historic buildings. The one above is the Loren Andrus Octagon House in Washington, Michigan USA, built in 1860.
Because they are based on a regular octagon, opposite walls are parallel and the rooms have a pleasing symmetry.