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A Regular Polygon with 63 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 63 sides where the length of each side is 3 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 63 sides. What are the interior angles and exterior angles? 
If the length of each side is 3 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 63

Perimeter of a polygon with 63 sides = (side length) x 63 = 189 units

Area of a polygon with 63 sides = (n x Sidecot (Π/n))/4 = (n x 3cot (Π/63))/4 = 2840.23 square units

Sum of the interior angles of a polygon with 63 sides = 
 (n-2) x 180 degrees =  (63-2) x 180 degrees = 10980 degrees

Interior Angle of a polygon with 63 sides = (n-2) x 180/n degrees = (63-2) x 180/63 degrees = 174.28 degrees 

Exterior angle of a polygon with 63 sides = 180 - Interior Angle = 180 - 174.28 = 5.71 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/63) = 3 x cot 2 = 60.11 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/63) = 3 x cosec 2 degrees = 60.18 units

Symmetry Group = D63  63 rotational symmetries and 63 reflection symmetries. The "D" stands for di-hedral. 




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