The Learning Point‎ > ‎Mathematics‎ > ‎Polygons‎ > ‎

A Regular Polygon with 60 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 60 sides where the length of each side is 4 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 60 sides. What are the interior angles and exterior angles? 
If the length of each side is 4 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 60

Perimeter of a polygon with 60 sides = (side length) x 60 = 240 units

Area of a polygon with 60 sides = (n x Sidecot (Π/n))/4 = (n x 4cot (Π/60))/4 = 4579.47 square units

Sum of the interior angles of a polygon with 60 sides = 
 (n-2) x 180 degrees =  (60-2) x 180 degrees = 10440 degrees

Interior Angle of a polygon with 60 sides = (n-2) x 180/n degrees = (60-2) x 180/60 degrees = 174 degrees 

Exterior angle of a polygon with 60 sides = 180 - Interior Angle = 180 - 174 = 6 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/60) = 4 x cot 3 = 76.32 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/60) = 4 x cosec 3 degrees = 76.42 units

Symmetry Group = D60  60 rotational symmetries and 60 reflection symmetries. The "D" stands for di-hedral. 




Comments