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A Regular Polygon with 34 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 34 sides where the length of each side is 5 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 34 sides. What are the interior angles and exterior angles? 
If the length of each side is 5 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 34

Perimeter of a polygon with 34 sides = (side length) x 34 = 170 units

Area of a polygon with 34 sides = (n x Sidecot (Π/n))/4 = (n x 5cot (Π/34))/4 = 2293.24 square units

Sum of the interior angles of a polygon with 34 sides = 
 (n-2) x 180 degrees =  (34-2) x 180 degrees = 5760 degrees

Interior Angle of a polygon with 34 sides = (n-2) x 180/n degrees = (34-2) x 180/34 degrees = 169.41 degrees 

Exterior angle of a polygon with 34 sides = 180 - Interior Angle = 180 - 169.41 = 10.58 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/34) = 5 x cot 5 = 53.95 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/34) = 5 x cosec 5 degrees = 54.18 units

Symmetry Group = D34  34 rotational symmetries and 34 reflection symmetries. The "D" stands for di-hedral. 




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