The Learning Point‎ > ‎Mathematics‎ > ‎Polygons‎ > ‎

A Regular Polygon with 55 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 55 sides where the length of each side is 3 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 55 sides. What are the interior angles and exterior angles? 
If the length of each side is 3 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 55

Perimeter of a polygon with 55 sides = (side length) x 55 = 165 units

Area of a polygon with 55 sides = (n x Sidecot (Π/n))/4 = (n x 3cot (Π/55))/4 = 2164.13 square units

Sum of the interior angles of a polygon with 55 sides = 
 (n-2) x 180 degrees =  (55-2) x 180 degrees = 9540 degrees

Interior Angle of a polygon with 55 sides = (n-2) x 180/n degrees = (55-2) x 180/55 degrees = 173.45 degrees 

Exterior angle of a polygon with 55 sides = 180 - Interior Angle = 180 - 173.45 = 6.54 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/55) = 3 x cot 3 = 52.46 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/55) = 3 x cosec 3 degrees = 52.54 units

Symmetry Group = D55  55 rotational symmetries and 55 reflection symmetries. The "D" stands for di-hedral. 




Comments