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11.5 Area of Regular Polygons

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.

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11.5 Area of Regular Polygons

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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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