11.5 Area of Regular Polygons

Theorem 106 Theorem 106: The area of an equilateral triangle equals the product of one- fourth the square of a side and the square root of three. Formula: A eq = √ 3, where “S” is the length of a side. 2 S 4

Example 1 Triangle ABC is an equilateral triangle with side lengths of 4. Solve for the area of the triangle. 4

Apothem An apothem is the segment drawn from the center of a regular polygon to the midpoint of any side. Example: Apothem

Theorem 107 Theorem 107: The area of a regular polygon equals the product of one-half of the apothem and the perimeter. Formula: A = ap, where a = the apothem poly 1 2

Example 2 Given a regular hexagon with side lengths of 18 and an apothem length of 9. Solve for the area of the hexagon. 18 9