Octagon eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° (formula_1 radians). The central angle is 45° (formula_2 radians). The area of a regular octagon of side length "a" is given by In terms of the circumradius "R", the area is In terms of the apothem "r" (see also inscribed figure), the area is These last two coefficients bracket the value of pi, the area of the unit circle. The area can also be expressed as where
Octagon is then as above: Expressed in terms of the span, the area is Another simple formula for the area is More often the span "S" is known, and the length of the sides, "a", is to be determined, as when cutting a square piece of material into a regular octagon. From the above, The two end lengths "e" on each side (the leg lengths of the triangles (green in the image) truncated from the square), as well as being formula_12 may be calculated as The circumradius of the regular octagon in terms of the side length "a" is and the