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Mastering Regular Polygon Formulas: Radius, Apothem, Perimeter, and Area

Understand how to calculate radius, apothem, perimeter, and area of various regular polygons. Learn examples and formulas for accurate measurements and geometric calculations.

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Mastering Regular Polygon Formulas: Radius, Apothem, Perimeter, and Area

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  1. 11.3 Vocabulary Radius of a Regular Polygon Apothem of a Regular Polygon

  2. Perimeter and Area Formulas you should be familiar with…

  3. NOTE: This area formula works for ANY quadrilateral with perpendicular diagonals

  4. EXAMPLE 1B: Given Rhombus RHOM with a perimeter = 52 and one diagonal length = 24, find the length of the second diagonal and the area of RHOM

  5. The center of a regular polygonis equidistant from the vertices. The distance from the center to a vertice is called the radius of the polygon. The apothemis the distance from the center to a side. A central angle of a regular polygonhas its vertex at the center, and its sides pass through consecutive vertices. Each central angle measure of a regular n-gon = Regular pentagon DEFGH has a center C, apothem BC, central angle DCE and r = CD.

  6. area of each triangle: total area of the polygon: To find the area of a regular n-gon with side length s and apothem a, divide it into n congruent isosceles triangles.

  7. Note: If you draw one of the triangles with the central angle, the apothem, the radius, and the side length you can use the Pythagorean theorem or trigonometry to calculate the missing pieces.

  8. MK = 1.368, LM = 3.759 s = 2(1.368) = 2.736 Nonagon (n = 9) so Perimeter is 9(2.736) = 24.624 A = ½ aP A= ½ (3.759)(24.624) A = 46.3

  9. EXAMPLES: • 1. Find the area of a regular octagon with r = 12 and s = 9.2 • 2. Find the area of a regular pentagon with s = 10

  10. EXAMPLES: • 3. Find the area of a regular hexagon with s = 6 • 4. Find the area of a regular hexagon with a = 10

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