Construction and Elementary Properties
A regular octagon may be constructed as follows:
- Draw a circle and a diameter AOB, where O is the center and A,B are points on the circumference.
- Draw another diameter COD, perpendicular to AOB.
- (Note in passing that A,B,C,D are vertices of a square).
- Draw the bisectors of the right angles AOC and BOC, making two more diameters EOF and GOH.
- A,B,C,D,E,F,G,H are the vertices of the octagon.
Each side of a regular octagon subtends half a right angle at the centre of the circle which connects its vertices. Its area can thus be computed as the sum of 8 isosceles triangles, leading to the result: Area = 2*a*a*(sqrt(2) + 1) for an octagon of side a.
Read more about this topic: Octagon
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