SOLUTION: I have an 8 sided figure that is 146 inches in diameter. Assuming all the sides are equal in length, was is the length of one of the sides? And what is the basic area (It's a gazeb

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Question 340674: I have an 8 sided figure that is 146 inches in diameter. Assuming all the sides are equal in length, was is the length of one of the sides? And what is the basic area (It's a gazebo and I'm trying to figure out what will fit in it!) Thank you.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I have an 8 sided figure that is 146 inches in diameter. Assuming all the sides are equal in length, was is the length of one of the sides? And what is the basic area (It's a gazebo and I'm trying to figure out what will fit in it!)
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Assuming the 146 is from point to point:
s = (146/2)*sin(22.5)
s =~ 27.94 inches (side length)
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Area = ns^2*cot(180/n)/4 n = 8, # of sides
Area =~ 3768 sq in =~ 26.17 sq feet

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


That depends. Did you measure the "diameter" from vertex to vertex, or from the middle of one of the sides to the other side?

Presuming 146 is the diameter of the circumcircle (circle around the outside, touching all the vertices):

inches

square inches which is to say approximately square feet.

If you meant the other way, write back and I'll work that out for you.

John

My calculator said it, I believe it, that settles it