Octagon

An octagon is an 8-sided polygon (a flat shape with straight sides).

First, have a play with an octagon:

images/area-coords.js?mode=8

Regular or Irregular

When all angles are equal and all sides are equal it is regular, otherwise it is irregular

Regular octagon with eight equal sides and equal internal angles
Regular Octagon
Irregular convex octagon with sides of different lengths   Irregular concave octagon with one corner pointing inward
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)

Irregular convex octagon with sides of different lengths
Convex Octagon
Irregular concave octagon with one corner pointing inward
Concave Octagon

Is it an Octagon?

An octagon has 8 straight sides. The shape must also be closed (all the lines connect up):

Irregular convex octagon with sides of different lengths
Octagon
(straight sides)
An eight-sided shape where one side is curved, so it isn't an octagon
Not an Octagon
(has a curve)
An open shape made of eight lines that don't connect to close the shape
Not an Octagon
(open, not closed)

Properties

A regular octagon with side length "s" has:

Regular octagon diagram showing an interior angle of 135 degrees and exterior angle of 45 degrees

Any octagon has:

Standard red stop sign, which is a real-world example of a regular octagon
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