Reckoning / Shape / Regular octagon
Plane figure · Polygons
Regular octagon
Eight equal sides and angles; a square with its corners cut off at 45°.
Dimensions
Results
area A
width across flats w
Formulas
A square of side w = s(1 + √2) minus four corner triangles with legs s/√2.
Checked: the A formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.
Topology lens
Topologically a disc, like every figure here without a hole: Euler characteristic 1. Stretching turns it into a circle, a square or a star. More on the lens.