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A Regular Polygon with 113 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 113 sides where the length of each side is 7 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 113 sides. What are the interior angles and exterior angles? 
If the length of each side is 7 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 113

Perimeter of a polygon with 113 sides = (side length) x 113 = 791 units

Area of a polygon with 113 sides = (n x Sidecot (Π/n))/4 = (n x 7cot (Π/113))/4 = 49777.28 square units

Sum of the interior angles of a polygon with 113 sides = 
 (n-2) x 180 degrees =  (113-2) x 180 degrees = 19980 degrees

Interior Angle of a polygon with 113 sides = (n-2) x 180/n degrees = (113-2) x 180/113 degrees = 176.81 degrees 

Exterior angle of a polygon with 113 sides = 180 - Interior Angle = 180 - 176.81 = 3.18 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/113) = 7 x cot 1 = 251.71 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/113) = 7 x cosec 1 degrees = 251.81 units

Symmetry Group = D113  113 rotational symmetries and 113 reflection symmetries. The "D" stands for di-hedral. 




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