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A Regular Polygon with 139 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 139 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 139 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 = 139

Perimeter of a polygon with 139 sides = (side length) x 139 = 417 units

Area of a polygon with 139 sides = (n x Sidecot (Π/n))/4 = (n x 3cot (Π/139))/4 = 13835.29 square units

Sum of the interior angles of a polygon with 139 sides = 
 (n-2) x 180 degrees =  (139-2) x 180 degrees = 24660 degrees

Interior Angle of a polygon with 139 sides = (n-2) x 180/n degrees = (139-2) x 180/139 degrees = 177.41 degrees 

Exterior angle of a polygon with 139 sides = 180 - Interior Angle = 180 - 177.41 = 2.58 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/139) = 3 x cot 1 = 132.71 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/139) = 3 x cosec 1 degrees = 132.74 units

Symmetry Group = D139  139 rotational symmetries and 139 reflection symmetries. The "D" stands for di-hedral. 




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