SOLUTION: What is the perimeter of the largest regular pentagon that can be inscribed in a circle whose circumference is 256pi ft. ?

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Question 1014093: What is the perimeter of the largest regular pentagon that can be inscribed in a circle whose circumference is 256pi ft. ?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Since C%22%22=%22%222%2Api%2Ar
      256pi%22%22=%22%222%2Api%2Ar
      %28256pi%29%2F%282pi%29%22%22=%22%22r 
      128%22%22=%22%22r 

Each interior angle of a regular polygon is %28%28n-2%29%2A%22180%B0%22%29%2Fn,
where n is the number of sides.  Here n=5 so each interior angle
is %28%285-2%29%28%22180%B0%22%29%29%2F5%22%22=%22%22%283%2A%22180%B0%22%29%2F5%22%22=%22%22%22108%B0%22.
The marked angle below is one-half of an interior angle so it is %2254%B0%22. 
the line segment marked x is one-half of a side of the pentagon.  



Edwin