A Regular Polygon with 82 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius

You are given a Regular Polygon with 82 sides. What are the interior angles and exterior angles?

If the length of each side is 8 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 82

Perimeter of a polygon with 82 sides = (side length) x 82 = 656 units

Area of a polygon with 82 sides = (n x Side²x cot (Π/n))/4 = (n x 8²x cot (Π/82))/4 = 34228.29 square units

Sum of the interior angles of a polygon with 82 sides = (n-2) x 180 degrees = (82-2) x 180 degrees = 14400 degrees

Interior Angle of a polygon with 82 sides = (n-2) x 180/n degrees = (82-2) x 180/82 degrees = 175.6 degrees

Exterior angle of a polygon with 82 sides = 180 - Interior Angle = 180 - 175.6 = 4.39 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/82) = 8 x cot 2 = 208.7 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/82) = 8 x cosec 2 degrees = 208.86 units

Symmetry Group = D₈₂ 82 rotational symmetries and 82 reflection symmetries. The "D" stands for di-hedral.

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