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A Regular Polygon with 20 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 20 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 20 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 = 20

Perimeter of a polygon with 20 sides = (side length) x 20 = 140 units

Area of a polygon with 20 sides = (n x Sidecot (Π/n))/4 = (n x 7cot (Π/20))/4 = 1546.86 square units

Sum of the interior angles of a polygon with 20 sides = 
 (n-2) x 180 degrees =  (20-2) x 180 degrees = 3240 degrees

Interior Angle of a polygon with 20 sides = (n-2) x 180/n degrees = (20-2) x 180/20 degrees = 162 degrees 

Exterior angle of a polygon with 20 sides = 180 - Interior Angle = 180 - 162 = 18 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/20) = 7 x cot 9 = 44.19 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/20) = 7 x cosec 9 degrees = 44.74 units

Symmetry Group = D20  20 rotational symmetries and 20 reflection symmetries. The "D" stands for di-hedral. 




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