Answer:
42
Explanation:
A regular polygon with 42 sides where the length of each side is 2 units. The units may either be inches or cm or km or miles: any unit of length.
You are given a Regular Polygon with 42 sides. What are the interior angles and exterior angles?
If the length of each side is 2 units, what is the perimeter, area, circum-radius and in-radius of the polygon?
n = 42
Perimeter of a polygon with 42 sides = (side length) x 42 = 84 units
Area of a polygon with 42 sides = (n x Side2 x cot (Π/n))/4 = (n x 22 x cot (Π/42))/4 = 560.45 square units
Sum of the interior angles of a polygon with 42 sides = (n-2) x 180 degrees = (42-2) x 180 degrees = 7200 degrees
Interior Angle of a polygon with 42 sides = (n-2) x 180/n degrees = (42-2) x 180/42 degrees = 171.42 degrees
Exterior angle of a polygon with 42 sides = 180 - Interior Angle = 180 - 171.42 = 8.57 degrees
Inradius = Radius of In-circle = (side length) x cot (Π/42) = 2 x cot 4 = 26.68 units
Circumradius = Radius of Circum-circle = (side length) x cosec (Π/42) = 2 x cosec 4 degrees = 26.76 units
Symmetry Group = D42 42 rotational symmetries and 42 reflection symmetries. The "D" stands for di-hedral.