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A Regular Polygon with 19 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 19 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 19 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 = 19

Perimeter of a polygon with 19 sides = (side length) x 19 = 152 units

Area of a polygon with 19 sides = (n x Sidecot (Π/n))/4 = (n x 8cot (Π/19))/4 = 1821.77 square units

Sum of the interior angles of a polygon with 19 sides = 
 (n-2) x 180 degrees =  (19-2) x 180 degrees = 3060 degrees

Interior Angle of a polygon with 19 sides = (n-2) x 180/n degrees = (19-2) x 180/19 degrees = 161.05 degrees 

Exterior angle of a polygon with 19 sides = 180 - Interior Angle = 180 - 161.05 = 18.94 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/19) = 8 x cot 9 = 47.94 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/19) = 8 x cosec 9 degrees = 48.6 units

Symmetry Group = D19  19 rotational symmetries and 19 reflection symmetries. The "D" stands for di-hedral. 




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