Building a Circle from 31 Panels: Calculating Circumference & Diameter

[Somnabulist]

I am not a student but should become one again as I apparently did not learn enough in school. I am faced with a real world question I do not know how to answer using mathematics. Here is the problem without too much physical detail:

I need to construct a circle (rough circle) out of 31 panels that are 12 feet long. They are connectable with zero clearance. In addition is a gate that is 6 feet wide. How would I compute the diameter or the circumfrance of this circle? Is this enough data to compute an answer?

Another way to ask this is what is the circumfrance or the diameter of a circle made from a line that is 378 feet long?

 

[Mark44]

If you have a line segment that is 378 feet long and you bend it to form a circle, the circumference of the circle will be 378 feet. The diameter of a circle is given by d = C/[itex]\pi[itex], where C is the circumference.

Your 31 panels plus the gate will form a 32-sided polygon that is not a circle, but is roughly circular in shape. The 378' perimeter of this figure will be approximately the same as the circumference of the corresponding circle.

Is that what you're looking for?

 

[Somnabulist]

If you have a line segment that is 378 feet long and you bend it to form a circle, the circumference of the circle will be 378 feet. The diameter of a circle is given by d = C/[itex]\pi[itex], where C is the circumference.

Your 31 panels plus the gate will form a 32-sided polygon that is not a circle, but is roughly circular in shape. The 378' perimeter of this figure will be approximately the same as the circumference of the corresponding circle.

Is that what you're looking for?

Now this is why it is important to teach logic in school; length of line equals circumfrance of a circle made from that line. Yes, it is a 32 sided polygon in a rough circle shape. That is what I was looking for. I will be spending more time in remdial education on this website. Thanks for the taking the time to answer.