A Regular Polygon with 23 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius

You are given a Regular Polygon with 23 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 = 23

Perimeter of a polygon with 23 sides = (side length) x 23 = 184 units

Area of a polygon with 23 sides = (n x Side²x cot (Π/n))/4 = (n x 8²x cot (Π/23))/4 = 2677.39 square units

Sum of the interior angles of a polygon with 23 sides = (n-2) x 180 degrees = (23-2) x 180 degrees = 3780 degrees

Interior Angle of a polygon with 23 sides = (n-2) x 180/n degrees = (23-2) x 180/23 degrees = 164.34 degrees

Exterior angle of a polygon with 23 sides = 180 - Interior Angle = 180 - 164.34 = 15.65 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/23) = 8 x cot 7 = 58.2 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/23) = 8 x cosec 7 degrees = 58.75 units

Symmetry Group = D₂₃ 23 rotational symmetries and 23 reflection symmetries. The "D" stands for di-hedral.

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