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A Regular Polygon with 22 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 22 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 22 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 = 22

Perimeter of a polygon with 22 sides = (side length) x 22 = 220 units

Area of a polygon with 22 sides = (n x Sidecot (Π/n))/4 = (n x 10cot (Π/22))/4 = 3825.33 square units

Sum of the interior angles of a polygon with 22 sides = 
 (n-2) x 180 degrees =  (22-2) x 180 degrees = 3600 degrees

Interior Angle of a polygon with 22 sides = (n-2) x 180/n degrees = (22-2) x 180/22 degrees = 163.63 degrees 

Exterior angle of a polygon with 22 sides = 180 - Interior Angle = 180 - 163.63 = 16.36 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/22) = 10 x cot 8 = 69.55 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/22) = 10 x cosec 8 degrees = 70.26 units

Symmetry Group = D22  22 rotational symmetries and 22 reflection symmetries. The "D" stands for di-hedral. 




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