Polygon Formulas - 9th Geometry

Formula for: finding a polygon’s interior angles

(n-2)x180 [where “n” = # of sides]

Formula for: the angle measure of an exterior angle (regular polygon)

m< = 360/n [where “n” = # of sides]

Why does (n-2)x180 work to find interior angles?

This works because “n” is the sides, and there’s the same amount of sides as angles in a regular polygon.

Formula for: finding the measure of the central angle

m< = 360/n

Formula for: finding the radius of a regular polygon

apothem/cos(360/2n)

Why does the “(360/2n)” part of the radius equation [“apothem/cos(360/2n)”] work?

Because it gives you half the central angle. 360/n would equal the full central angle, and you don’t want the full central angle if you want to make a right triangle with the radius and apothem line

Formula for: finding the apothem

(radius)x cos(360/2n)

Formula for: finding the perimeter of a regular polygon

# of sides x length of one side of the polygon

Formula for: finding the area of a triangle

Area = ½ x b x h

Formula for: finding the area of a regular polygon

Area [of one triangle] = ½ x b x h —> Area = n/2 x b x h [n = # of sides] —> Area = P x a / 2 [P= perimeter, a = apothem]

Formula for: finding the side length of a regular polygon

2(radius) sin(360/2n) = side length