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A Regular Polygon with 16 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 16 sides where the length of each side is 2 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 16 sides. What are the interior angles and exterior angles? 
If the length of each side is 2 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 16

Perimeter of a polygon with 16 sides = (side length) x 16 = 32 units

Area of a polygon with 16 sides = (n x Sidecot (Π/n))/4 = (n x 2cot (Π/16))/4 = 80.43 square units

Sum of the interior angles of a polygon with 16 sides = 
 (n-2) x 180 degrees =  (16-2) x 180 degrees = 2520 degrees

Interior Angle of a polygon with 16 sides = (n-2) x 180/n degrees = (16-2) x 180/16 degrees = 157.5 degrees 

Exterior angle of a polygon with 16 sides = 180 - Interior Angle = 180 - 157.5 = 22.5 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/16) = 2 x cot 11 = 10.05 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/16) = 2 x cosec 11 degrees = 10.25 units

Symmetry Group = D16  16 rotational symmetries and 16 reflection symmetries. The "D" stands for di-hedral. 




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