A Regular Polygon with 146 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius

You are given a Regular Polygon with 146 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 = 146

Perimeter of a polygon with 146 sides = (side length) x 146 = 1022 units

Area of a polygon with 146 sides = (n x Side²x cot (Π/n))/4 = (n x 7²x cot (Π/146))/4 = 83104.56 square units

Sum of the interior angles of a polygon with 146 sides = (n-2) x 180 degrees = (146-2) x 180 degrees = 25920 degrees

Interior Angle of a polygon with 146 sides = (n-2) x 180/n degrees = (146-2) x 180/146 degrees = 177.53 degrees

Exterior angle of a polygon with 146 sides = 180 - Interior Angle = 180 - 177.53 = 2.46 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/146) = 7 x cot 1 = 325.26 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/146) = 7 x cosec 1 degrees = 325.33 units

Symmetry Group = D₁₄₆ 146 rotational symmetries and 146 reflection symmetries. The "D" stands for di-hedral.

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