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A Regular Polygon with 3 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 3 sides where the length of each side is 3 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 3 sides. What are the interior angles and exterior angles? 
If the length of each side is 3 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 3

Perimeter of a polygon with 3 sides = (side length) x 3 = 9 units

Area of a polygon with 3 sides = (n x Sidecot (Π/n))/4 = (n x 3cot (Π/3))/4 = 3.89 square units

Sum of the interior angles of a polygon with 3 sides = 
 (n-2) x 180 degrees =  (3-2) x 180 degrees = 180 degrees

Interior Angle of a polygon with 3 sides = (n-2) x 180/n degrees = (3-2) x 180/3 degrees = 60 degrees 

Exterior angle of a polygon with 3 sides = 180 - Interior Angle = 180 - 60 = 120 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/3) = 3 x cot 60 = 1.73 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/3) = 3 x cosec 60 degrees = 3.46 units

Symmetry Group = D3  3 rotational symmetries and 3 reflection symmetries. The "D" stands for di-hedral. 




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