Octagon
An octagon is an 8-sided polygon (a flat shape with straight sides).
First, have a play with an octagon:
Regular or Irregular
When all angles are equal and all sides are equal it is regular, otherwise it is irregular
Regular Octagon | Irregular Octagons |
Concave or Convex
A convex octagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.
When any internal angle is greater than 180° it is concave. (Think: concave has a "cave" in it)
Convex Octagon | Concave Octagon |
Is it an Octagon?
An octagon has 8 straight sides. The shape must also be closed (all the lines connect up):
Octagon (straight sides) |
Not an Octagon (has a curve) |
Not an Octagon (open, not closed) |
Properties
A regular octagon has:
- Interior Angles of 135°
- Exterior Angles of 45°
- Area = 2(1+√2)s^{2}, or approximately 4.828427 × s^{2} (where s=side length)
- Width w = (1+√2)s
Any octagon has:
- Sum of Interior Angles of 1080°
- 20 diagonals