The Learning Point‎ > ‎Mathematics‎ > ‎Polygons‎ > ‎

A Regular Polygon with 74 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius



A regular polygon with 74 sides where the length of each side is 7 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 74 sides. What are the interior angles and exterior angles? 
If the length of each side is 7 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 74

Perimeter of a polygon with 74 sides = (side length) x 74 = 518 units

Area of a polygon with 74 sides = (n x Sidecot (Π/n))/4 = (n x 7cot (Π/74))/4 = 21339.71 square units

Sum of the interior angles of a polygon with 74 sides = 
 (n-2) x 180 degrees =  (74-2) x 180 degrees = 12960 degrees

Interior Angle of a polygon with 74 sides = (n-2) x 180/n degrees = (74-2) x 180/74 degrees = 175.13 degrees 

Exterior angle of a polygon with 74 sides = 180 - Interior Angle = 180 - 175.13 = 4.86 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/74) = 7 x cot 2 = 164.78 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/74) = 7 x cosec 2 degrees = 164.93 units

Symmetry Group = D74  74 rotational symmetries and 74 reflection symmetries. The "D" stands for di-hedral. 




Comments