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A Regular Polygon with 6 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 6 sides where the length of each side is 9 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 6 sides. What are the interior angles and exterior angles? 
If the length of each side is 9 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 6

Perimeter of a polygon with 6 sides = (side length) x 6 = 54 units

Area of a polygon with 6 sides = (n x Sidecot (Π/n))/4 = (n x 9cot (Π/6))/4 = 210.44 square units

Sum of the interior angles of a polygon with 6 sides = 
 (n-2) x 180 degrees =  (6-2) x 180 degrees = 720 degrees

Interior Angle of a polygon with 6 sides = (n-2) x 180/n degrees = (6-2) x 180/6 degrees = 120 degrees 

Exterior angle of a polygon with 6 sides = 180 - Interior Angle = 180 - 120 = 60 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/6) = 9 x cot 30 = 15.58 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/6) = 9 x cosec 30 degrees = 18 units

Symmetry Group = D6  6 rotational symmetries and 6 reflection symmetries. The "D" stands for di-hedral. 




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