I'll give this a try.

The angle from the center to a middle of one of the sides would be 22.5 (180/n). The radius of your octagon is 72", which would make this the adjacent side. What we need to figure out is the opposite side. Using a trigonometry function, we can find the opposite side by using 2 x radius x tan 22.5. This gives us 59.64675".

I'll let someone check my work. It's been a decade since I've done any trig.

Tai

By the way, I'm assuming 12' is going across.