A Regular Polygon with 5 sides: Area, Perimeter, Interior and Exterior Angles, Inradius, Circumradius

You are given a Regular Polygon with 5 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 = 5

Perimeter of a polygon with 5 sides = (side length) x 5 = 10 units

Area of a polygon with 5 sides = (n x Side²x cot (Π/n))/4 = (n x 2²x cot (Π/5))/4 = 6.88 square units

Sum of the interior angles of a polygon with 5 sides = (n-2) x 180 degrees = (5-2) x 180 degrees = 540 degrees

Interior Angle of a polygon with 5 sides = (n-2) x 180/n degrees = (5-2) x 180/5 degrees = 108 degrees

Exterior angle of a polygon with 5 sides = 180 - Interior Angle = 180 - 108 = 72 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/5) = 2 x cot 36 = 2.75 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/5) = 2 x cosec 36 degrees = 3.4 units

Symmetry Group = D₅ 5 rotational symmetries and 5 reflection symmetries. The "D" stands for di-hedral.

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