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A Regular Polygon with 150 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 150 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 150 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 = 150

Perimeter of a polygon with 150 sides = side x 150 = 600 units

Area of a polygon with 150 sides = (n x Sidecot (Π/n))/4 = (n x 4cot (Π/150))/4 = 28643.7 square units

Sum of the interior angles of a polygon with 150 sides = 
 (n-2) x 180 degrees =  (150-2) x 180 degrees = 26640 degrees

Interior Angle of a polygon with 150 sides = (n-2) x 180/n degrees = (150-2) x 180/150 degrees = 177.6 degrees 

Exterior angle of a polygon with 150 sides = 180 - Interior Angle = 180 - 177.6 = 2.4 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/150) = 4 x cot 1 = 190.95 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/150) = 4 x cosec 1 degrees = 190.99 units

Symmetry Group = D150  150 rotational symmetries and 150 reflection symmetries. The "D" stands for di-hedral. 




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