The Learning Point‎ > ‎Mathematics‎ > ‎Polygons‎ > ‎

A Regular Polygon with 140 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 140 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 140 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 = 140

Perimeter of a polygon with 140 sides = (side length) x 140 = 420 units

Area of a polygon with 140 sides = (n x Sidecot (Π/n))/4 = (n x 3cot (Π/140))/4 = 14035.1 square units

Sum of the interior angles of a polygon with 140 sides = 
 (n-2) x 180 degrees =  (140-2) x 180 degrees = 24840 degrees

Interior Angle of a polygon with 140 sides = (n-2) x 180/n degrees = (140-2) x 180/140 degrees = 177.42 degrees 

Exterior angle of a polygon with 140 sides = 180 - Interior Angle = 180 - 177.42 = 2.57 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/140) = 3 x cot 1 = 133.66 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/140) = 3 x cosec 1 degrees = 133.7 units

Symmetry Group = D140  140 rotational symmetries and 140 reflection symmetries. The "D" stands for di-hedral. 




Comments