A Regular Polygon with 24 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius

You are given a Regular Polygon with 24 sides. What are the interior angles and exterior angles?

If the length of each side is 4 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 24

Perimeter of a polygon with 24 sides = (side length) x 24 = 96 units

Area of a polygon with 24 sides = (n x Side²x cot (Π/n))/4 = (n x 4²x cot (Π/24))/4 = 729.19 square units

Sum of the interior angles of a polygon with 24 sides = (n-2) x 180 degrees = (24-2) x 180 degrees = 3960 degrees

Interior Angle of a polygon with 24 sides = (n-2) x 180/n degrees = (24-2) x 180/24 degrees = 165 degrees

Exterior angle of a polygon with 24 sides = 180 - Interior Angle = 180 - 165 = 15 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/24) = 4 x cot 7 = 30.38 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/24) = 4 x cosec 7 degrees = 30.64 units

Symmetry Group = D₂₄ 24 rotational symmetries and 24 reflection symmetries. The "D" stands for di-hedral.

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