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A Regular Polygon with 80 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 80 sides where the length of each side is 10 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 80 sides. What are the interior angles and exterior angles? 
If the length of each side is 10 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 80

Perimeter of a polygon with 80 sides = (side length) x 80 = 800 units

Area of a polygon with 80 sides = (n x Side2 x cot (Π/n))/4 = (n x 102 x cot (Π/80))/4 = 50903.39 square units

Sum of the interior angles of a polygon with 80 sides =  (n-2) x 180 degrees =  (80-2) x 180 degrees = 14040 degrees

Interior Angle of a polygon with 80 sides = (n-2) x 180/n degrees = (80-2) x 180/80 degrees = 175.5 degrees 

Exterior angle of a polygon with 80 sides = 180 - Interior Angle = 180 - 175.5 = 4.5 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/80) = 10 x cot 2 = 254.51 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/80) = 10 x cosec 2 degrees = 254.71 units

Symmetry Group = D80  80 rotational symmetries and 80 reflection symmetries. The "D" stands for di-hedral. 




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