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Regular Polygons: Apothem & Area Formula Presentation

Learn how to find the area of regular polygons using the apothem and side length properties. Discover the formula, examples, and practice problems to master this concept.

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Regular Polygons: Apothem & Area Formula Presentation

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  1. BELL RINGER • For the first 30 minutes of class, you will finish the assignment from our last session: • p.413, #1-9, p.418, #1-11 • E.C., p. 420, #20, 27 Then, each GROUP will be required to present a problem of my random choice from the assignment to the rest of the class. The presentation is worth 20 points.

  2. Presentation #1 • P.413, #6

  3. Presentation #2 • P. 413, #8

  4. Presentation #3 • P.418, #5

  5. Presentation #4 • P.418, #8

  6. Finding the AREA of Regular Polygons Using the Apothem and the Side Length

  7. Apothem • The apothem is the segment from the center of the polygon and perpendicular to a side of the polygon. Apothem

  8. Property of Regular Polygons • Every regular polygon may be divided into n number of congruent triangles, and a side length of s. Observe the octagon below. The height of each triangle is the apothem of the polygon. AΔ = b*h*1/2 = s*a*1/2

  9. Formula • Therefore, the area formula for any regular polygon, where a = apothem, s = side length, and n = the number of sides: A = (s*a*1/2) * n

  10. Example • Find the area of a regular pentagon if its apothem is 3cm and the side length is 4.4cm. (3 * 4.4 * ½) * 5 = 33cm2 Try p. 427, #1-3, 5, 7

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