octagon n : an eight-sided polygon
EtymologyFirst attested in 1656, from octagonos, from οκτάγωνος (oktágōnos), eight-angled, from ὀκτώ (okto), eight + γωνία (gonia), angle.
- A polygon with eight sides and eight angles.
polygon with eight sides and eight angles
In geometry, an octagon is a polygon that has eight sides. A regular octagon is represented by the Schläfli symbol .
A regular octagon is an octagon whose sides are all the same length and whose internal angles are all the same size. The internal angle at each vertex of a regular octagon is 135° and the sum of all the internal angles is 1080°.
The area of a regular octagon of side length a is given by
- A = 2 \cot \frac a^2 = 2(1+\sqrt)a^2 \simeq 4.828427 a^2.
- A = 4 \sin \frac R^2 = 2\sqrtR^2 \simeq 2.828427 R^2.
- A = 8 \tan \frac r^2 = 8(\sqrt-1)r^2 \simeq 3.3137085 r^2.
The area may also be found this way:
Given the span S the length of a side B is
- B = S/(1+\sqrt)./ ,S1 + S2 + S3 + S4 + S5 + S6 +S7 + S8