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A Regular Polygon with 69 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 69 sides where the length of each side is 8 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 69 sides. What are the interior angles and exterior angles? 
If the length of each side is 8 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 69

Perimeter of a polygon with 69 sides = (side length) x 69 = 552 units

Area of a polygon with 69 sides = (n x Sidecot (Π/n))/4 = (n x 8cot (Π/69))/4 = 24230.81 square units

Sum of the interior angles of a polygon with 69 sides = 
 (n-2) x 180 degrees =  (69-2) x 180 degrees = 12060 degrees

Interior Angle of a polygon with 69 sides = (n-2) x 180/n degrees = (69-2) x 180/69 degrees = 174.78 degrees 

Exterior angle of a polygon with 69 sides = 180 - Interior Angle = 180 - 174.78 = 5.21 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/69) = 8 x cot 2 = 175.58 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/69) = 8 x cosec 2 degrees = 175.76 units

Symmetry Group = D69  69 rotational symmetries and 69 reflection symmetries. The "D" stands for di-hedral. 




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