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Areas of Regular Polygons

Areas of Regular Polygons. Area of a Regular Polygon. If a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, A = ½ Pa. Radii – segments drawn from the center of the polygon to a vertex. Apothem – a segment drawn from the center point

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Areas of Regular Polygons

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  1. Areas of Regular Polygons

  2. Area of a Regular Polygon • If a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, • A = ½ Pa. Radii – segments drawn from the center of the polygon to a vertex Apothem – a segment drawn from the center point of a polygon perpendicular to the side of a polygon

  3. Facts about the apothem • It is always perpendicular to a side, forming a right triangle. • It intersects the side of the polygon at the midpoint of the side.

  4. Area of a Regular Polygon The perimeter of this regular polygon is 60. The apothem is 8. If the perimeter of a regular pentagon is 60, then each side is 12. 8 Now find the area A = ½ Pa A = ½ (60)(8) A = 240 units 2

  5. Work this problem Find the area of the regular polygon. 10 One side is 10 units, so the perimeter is 8 * 10 = 80 units 11 A = ½ Pa A = ½ (80) (11) A = 440 units 2

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