I love Google-
Let W be the width of the octagon W is also the diameter of the inscribed circle
S be the length of the side
A be the area
P be the perimeter
B be the dimension at right angles to the sides
C be the dimension at right angles from a side to the point of intersection at right angles
from the adjacent two sides
D be the dimension between opposing corners
D is also the diameter of the circumscribed circle
-P-
Then by Reekie's Theorem
S = 0.4142 W B = 0.2929 W
S = 1.4142 B W = 0.3018 P
W = 2.4142 S B = 0.7071 S
W = 3.4142 B D = 1.0824 W
A = 0.8284 W2 P = 3.3137 W
W = 4.8284 C S = 0.3826 D
C = 0.2071 W W = 0.9239 D
W = The square root of 1.2071 A D = 2.6135 S
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W = S + 2B S = W - 2B
A = W2 - 2B2
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Doug
Edit-I googled and found the same site you gave and prepared the post but got called away. When I came back I posted it and found you had already suggested it. Thanks!
Doug