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Area Calculation in Regular Polygons: Equilateral Triangle and Apothem Method

Learn how to calculate the area of regular polygons using Theorem 106 for equilateral triangles and Theorem 107 for apothem length. Explore formulas and examples to master polygon area computations.

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Area Calculation in Regular Polygons: Equilateral Triangle and Apothem Method

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  1. 11.5 Area of Regular Polygons

  2. 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: Aeq = √3 , where “S” is the length of a side. 2 S 4

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

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

  5. 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 1 poly 2

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

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