The Learning Point‎ > ‎Mathematics‎ > ‎Polygons‎ > ‎

A Regular Polygon with 37 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 37 sides where the length of each side is 5 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 37 sides. What are the interior angles and exterior angles? 
If the length of each side is 5 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 37

Perimeter of a polygon with 37 sides = (side length) x 37 = 185 units

Area of a polygon with 37 sides = (n x Sidecot (Π/n))/4 = (n x 5cot (Π/37))/4 = 2716.99 square units

Sum of the interior angles of a polygon with 37 sides = 
 (n-2) x 180 degrees =  (37-2) x 180 degrees = 6300 degrees

Interior Angle of a polygon with 37 sides = (n-2) x 180/n degrees = (37-2) x 180/37 degrees = 170.27 degrees 

Exterior angle of a polygon with 37 sides = 180 - Interior Angle = 180 - 170.27 = 9.72 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/37) = 5 x cot 4 = 58.74 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/37) = 5 x cosec 4 degrees = 58.95 units

Symmetry Group = D37  37 rotational symmetries and 37 reflection symmetries. The "D" stands for di-hedral. 




Comments