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Area of Regular Polygons

Area of Regular Polygons. A regular polygon has all sides and all angles congruent. You can circumscribe a circle about any regular polygon. The center of the circle is the center of the regular polygon. The radius of a regular polygon is the distance from the center to a vertex.

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Area of Regular Polygons

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  1. Area of Regular Polygons • A regular polygon has all sides and all angles congruent. • You can circumscribe a circle about any regular polygon. The center of the circle is the center of the regular polygon. • The radius of a regular polygonis the distance from the center to a vertex. • The apothem of a regular polygon is the perpendicular distance from the center to the sides.

  2. A = Area of Regular Polygons The area of a regular polygon is half the product of the perimeter (p) and the apothem (a).

  3. 12.3” 8” Example 1 Find the area of a regular decathon with a 12.3 inch apothem and 8 inch sides. A = ½ ap p = 10(8) = 80” A = (½) (12.3) (80) = 492 sq. in.

  4. 10 cm long keg cm = a Example 2 Find the area of a regular hexagon with 10cm sides. The radii of a regular hexagon form 60 angles at the center. We can use the 30-60-90 triangle to find the apothem: short leg = 5 cm p = 6(s) = 60 cm

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