What does a regular octagon look like?

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)

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:

Any octagon has:

• Sum of Interior Angles of 1080°
• 20 diagonals

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An octagon is a polygon having eight sides and eight angles. It has eight vertices and eight edges that are joined end to end to form a close geometric shape.

An octagon-shape symbolizes rebirth, regeneration, transition, and infinity. The word ‘octagon’ is derived from the Greek words ‘okta’ meaning ‘eight’ and ‘gon’ meaning ‘side; angle’.

When all the eight sides and eight angles of an octagon are equal, it is a regular octagon. Otherwise, it is an irregular octagon.

The below-given properties and formulas to find the perimeter, area and length of diagonals only apply to the regular octagon.

Properties

1. Has 8 sides of equal length; in octagon ABCDEFGH, AB = BC = CD = DE = EF = FG = GH = HA
2. Has 8 interior angles each measuring 135°; so ∠ABC = ∠BCD = ∠CDE = ∠DEF = ∠EFG =∠FGH = ∠GHA = ∠HAB
3. The sum of all eight interior angles is 1080°; so ∠ABC + ∠BCD + ∠CDE + ∠DEF + ∠EFG +∠FGH + ∠GHA + ∠HAB = 1080°
4. Has 8 exterior angles, each measuring 45°
5. Has 20 diagonals; example AC, BD, CE, DH, EH, and FH

The formula for finding the perimeter of an octagon is given below:

• The street stop sign.
• The Tower of the Winds in Athens, Greece is the oldest known octagonal building. Some other popular octagonal buildings are Dome of the Rock (Jerusalem, Isreal), Octagon (Roosevelt Island, in New York), Baptistery (Albenga, Italy), and Liaodi Pagoda (China) among many others. 
• Objects in our daily life such as octagonal-shaped windows, floor tiles, lawn, clock, candles, and mirrors.

• More Resources
  • Area of Octagon
  • Concave and Convex Octagon 

Last modified on September 6th, 2022