The Learning Point‎ > ‎Mathematics‎ > ‎Polygons‎ > ‎

A Regular Polygon with 131 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 131 sides where the length of each side is 10 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 131 sides. What are the interior angles and exterior angles? 
If the length of each side is 10 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 131

Perimeter of a polygon with 131 sides = (side length) x 131 = 1310 units

Area of a polygon with 131 sides = (n x Sidecot (Π/n))/4 = (n x 10cot (Π/131))/4 = 136536.71 square units

Sum of the interior angles of a polygon with 131 sides = 
 (n-2) x 180 degrees =  (131-2) x 180 degrees = 23220 degrees

Interior Angle of a polygon with 131 sides = (n-2) x 180/n degrees = (131-2) x 180/131 degrees = 177.25 degrees 

Exterior angle of a polygon with 131 sides = 180 - Interior Angle = 180 - 177.25 = 2.74 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/131) = 10 x cot 1 = 416.9 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/131) = 10 x cosec 1 degrees = 417.02 units

Symmetry Group = D131  131 rotational symmetries and 131 reflection symmetries. The "D" stands for di-hedral. 




Comments