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Construction

A regular octagon at a given circumcircle may be constructed as follows:

A regular octagon can be constructed using a straightedge and a compass, as 8 = 2, a power of two:

The regular octagon can be constructed with meccano bars. Twelve bars of size 4, three bars of size 5 and two bars of size 6 are required.

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 eight isosceles triangles, leading to the result:

for an octagon of side a.