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A Regular Polygon with 17 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 17 sides where the length of each side is 7 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 17 sides. What are the interior angles and exterior angles? 
If the length of each side is 7 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 17

Perimeter of a polygon with 17 sides = (side length) x 17 = 119 units

Area of a polygon with 17 sides = (n x Sidecot (Π/n))/4 = (n x 7cot (Π/17))/4 = 1114.03 square units

Sum of the interior angles of a polygon with 17 sides = 
 (n-2) x 180 degrees =  (17-2) x 180 degrees = 2700 degrees

Interior Angle of a polygon with 17 sides = (n-2) x 180/n degrees = (17-2) x 180/17 degrees = 158.82 degrees 

Exterior angle of a polygon with 17 sides = 180 - Interior Angle = 180 - 158.82 = 21.17 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/17) = 7 x cot 10 = 37.44 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/17) = 7 x cosec 10 degrees = 38.09 units

Symmetry Group = D17  17 rotational symmetries and 17 reflection symmetries. The "D" stands for di-hedral. 




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