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A Regular Polygon with 66 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 66 sides where the length of each side is 6 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 66 sides. What are the interior angles and exterior angles? 
If the length of each side is 6 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 66

Perimeter of a polygon with 66 sides = (side length) x 66 = 396 units

Area of a polygon with 66 sides = (n x Sidecot (Π/n))/4 = (n x 6cot (Π/66))/4 = 12469.59 square units

Sum of the interior angles of a polygon with 66 sides = 
 (n-2) x 180 degrees =  (66-2) x 180 degrees = 11520 degrees

Interior Angle of a polygon with 66 sides = (n-2) x 180/n degrees = (66-2) x 180/66 degrees = 174.54 degrees 

Exterior angle of a polygon with 66 sides = 180 - Interior Angle = 180 - 174.54 = 5.45 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/66) = 6 x cot 2 = 125.95 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/66) = 6 x cosec 2 degrees = 126.09 units

Symmetry Group = D66  66 rotational symmetries and 66 reflection symmetries. The "D" stands for di-hedral. 




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