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A Regular Polygon with 30 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 30 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 30 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 = 30

Perimeter of a polygon with 30 sides = (side length) x 30 = 300 units

Area of a polygon with 30 sides = (n x Sidecot (Π/n))/4 = (n x 10cot (Π/30))/4 = 7135.77 square units

Sum of the interior angles of a polygon with 30 sides = 
 (n-2) x 180 degrees =  (30-2) x 180 degrees = 5040 degrees

Interior Angle of a polygon with 30 sides = (n-2) x 180/n degrees = (30-2) x 180/30 degrees = 168 degrees 

Exterior angle of a polygon with 30 sides = 180 - Interior Angle = 180 - 168 = 12 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/30) = 10 x cot 6 = 95.14 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/30) = 10 x cosec 6 degrees = 95.66 units

Symmetry Group = D30  30 rotational symmetries and 30 reflection symmetries. The "D" stands for di-hedral. 




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