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A Regular Polygon with 64 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 64 sides where the length of each side is 2 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 64 sides. What are the interior angles and exterior angles? 
If the length of each side is 2 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 64

Perimeter of a polygon with 64 sides = (side length) x 64 = 128 units

Area of a polygon with 64 sides = (n x Sidecot (Π/n))/4 = (n x 2cot (Π/64))/4 = 1302.74 square units

Sum of the interior angles of a polygon with 64 sides = 
 (n-2) x 180 degrees =  (64-2) x 180 degrees = 11160 degrees

Interior Angle of a polygon with 64 sides = (n-2) x 180/n degrees = (64-2) x 180/64 degrees = 174.37 degrees 

Exterior angle of a polygon with 64 sides = 180 - Interior Angle = 180 - 174.37 = 5.62 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/64) = 2 x cot 2 = 40.71 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/64) = 2 x cosec 2 degrees = 40.76 units

Symmetry Group = D64  64 rotational symmetries and 64 reflection symmetries. The "D" stands for di-hedral. 




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