Question from mark, a parent:

I need to know the measurements of an octagon with a inside diameter of 34.5 inches from side to side

Hi Mark,

Suppose the distance from side to side of a regular octagon is d units and the length of a side is s units.

From the diagram d = s + 2x. Triangle ABC is a right triangle so Pythagoras theorem states that

s^{2} = x^{2} + x^{2} = 2x^{2}

or

x = s/√2

Thus

d = s + 2x = s + 2s/√2 = s(1 + 2/√2) = (1 + √2) s

s = 1/(1 + √2) d

Penny