SOLUTION: Central angle of a polygon=10 degrees Perimeter= 108 cm What is the area

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Question 1075851: Central angle of a polygon=10 degrees
Perimeter= 108 cm
What is the area
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Central angle of a polygon=10 degrees
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--> 360/10 = 36 sides.
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Perimeter= 108 cm
108/36 = 3 = side length.
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What is the area
Area = ns%5E2%2Acot%28180%2Fn%29%2F4 where n + # of sides, s = side length
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Just calculator work now.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
I will assume that the polygon is a REGULAR polygon. 

The number of sides is 360%2F10 = 36.


The side length is 108%2F36 = 3 cm.


The apothem "a" is  3%2Fa = tan%2810%5Eo%2F2%29 = tan(5°),  or  a = 3%2Ftan%285%5Eo%29.


Then the area = %28P%2Aa%29%2F2 = %28108%2A3%29%2F%28%28%282%2A3%29%2Ftan%285%5Eo%29%29%29%29 = 54*tan(5°) cm%5E2.


I leave it to you to calculate the number.