The Learning Point‎ > ‎Mathematics‎ > ‎Polygons‎ > ‎

A Regular Polygon with 122 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 122 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 122 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 = 122

Perimeter of a polygon with 122 sides = (side length) x 122 = 1098 units

Area of a polygon with 122 sides = (n x Sidecot (Π/n))/4 = (n x 9cot (Π/122))/4 = 95917.71 square units

Sum of the interior angles of a polygon with 122 sides = 
 (n-2) x 180 degrees =  (122-2) x 180 degrees = 21600 degrees

Interior Angle of a polygon with 122 sides = (n-2) x 180/n degrees = (122-2) x 180/122 degrees = 177.04 degrees 

Exterior angle of a polygon with 122 sides = 180 - Interior Angle = 180 - 177.04 = 2.95 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/122) = 9 x cot 1 = 349.42 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/122) = 9 x cosec 1 degrees = 349.54 units

Symmetry Group = D122  122 rotational symmetries and 122 reflection symmetries. The "D" stands for di-hedral. 




Comments