Regular Octagon Problem

Date: 09/03/2005 at 15:28:34
From: John
Subject: Length of the sides of a Octagon given

What are the lengths of the sides of a regular octagon if the distance 
between opposing sides is 20 feet?

Date: 09/04/2005 at 00:16:11
From: Doctor Julien
Subject: Re: Length of the sides of a Octagon given

Hello John,

Let's take a look at the top of the octagon.  It looks something like
this:

       -----
     /       \
    /         \     
  A|           |B
   |           |

We know the distance between A and B is 20.  So let's just draw the 
top 3 sides.

         x  
       -----
   x /       \ x
    /_________\     
        20  

We know the angle between the sides with length x is 135 degrees.  Can
you figure out what x must be from here?

(Hint: Divide the figure above into a rectangle and two isosceles 
right triangles.)

- Doctor Julien, The Math Forum
  http://mathforum.org/dr.math/