Math CentralQuandaries & Queries


Question from Lewis:

How do I calculate the dimension of the diameter of an Octagon when each leg has a dimension of 60 feet?

Hi Lewis,

I assume you mean a regular octagon where all the sides have the same length and all the angles have the same measure.


In my diagram the diameter is d and the side length is s. From the diagram you can see that

d = s + 2x

Since you know that s = 60 feet all that remains is to find x. This we can do using Pythagoras Theorem. The small triangles with sides of length x, x and s are right triangles so, using Pythagoras Theorem,

s2 = x2 + x2 = 2x2


x = s/√2


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

In your case s = 60 feet so

d = (1 + √2) × 60 = 144.85 feet.


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