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A Regular Polygon with 149 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 149 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 149 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 = 149

Perimeter of a polygon with 149 sides = side x 149 = 1192 units

Area of a polygon with 149 sides = (n x Sidecot (Π/n))/4 = (n x 8cot (Π/149))/4 = 113052 square units

Sum of the interior angles of a polygon with 149 sides = 
 (n-2) x 180 degrees =  (149-2) x 180 degrees = 26460 degrees

Interior Angle of a polygon with 149 sides = (n-2) x 180/n degrees = (149-2) x 180/149 degrees = 177.58 degrees 

Exterior angle of a polygon with 149 sides = 180 - Interior Angle = 180 - 177.58 = 2.41 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/149) = 8 x cot 1 = 379.36 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/149) = 8 x cosec 1 degrees = 379.45 units

Symmetry Group = D149  149 rotational symmetries and 149 reflection symmetries. The "D" stands for di-hedral. 




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