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A Regular Polygon with 83 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 83 sides where the length of each side is 4 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 83 sides. What are the interior angles and exterior angles? 
If the length of each side is 4 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 83

Perimeter of a polygon with 83 sides = (side length) x 83 = 332 units

Area of a polygon with 83 sides = (n x Sidecot (Π/n))/4 = (n x 4cot (Π/83))/4 = 8767.15 square units

Sum of the interior angles of a polygon with 83 sides = 
 (n-2) x 180 degrees =  (83-2) x 180 degrees = 14580 degrees

Interior Angle of a polygon with 83 sides = (n-2) x 180/n degrees = (83-2) x 180/83 degrees = 175.66 degrees 

Exterior angle of a polygon with 83 sides = 180 - Interior Angle = 180 - 175.66 = 4.33 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/83) = 4 x cot 2 = 105.62 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/83) = 4 x cosec 2 degrees = 105.7 units

Symmetry Group = D83  83 rotational symmetries and 83 reflection symmetries. The "D" stands for di-hedral. 




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