1. Areas of Regular Polygons Section 11.6

4. Basic Terms

10. Areas of Regular Polygons Center of a regular polygon: center of the circumscribed circle. Radius: distance from the center to a vertex. Apothem: Perpendicular distance from the center to a side. Example 1: Find the measure of each numbered angle. • 1 2 3 360/5 = 72 ½ (72) = 36 L 2 = 36 L 3 = 54 L 1 = 72 Example 2: Find the area of a regular decagon with a 12.3 in apothem and 8 in sides. Area of a regular polygon: A = ½ a p where a is the apothem and p is the perimeter. Perimeter: 80 in A = ½ • 12.3 • 80 A = 492 in 2 Example 3: Find the area. 10 mm • A = ½ a p p = 60 mm 5 mm LL = √3 • 5 = 8.66 a A = ½ • 8.66 • 60 A = 259.8 mm 2

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