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Areas of Regular Polygons

Areas of Regular Polygons. Students will be able to find the areas of regular polygons. Regular Polygons. In this chapter we will be dealing only with regular polygons . Anytime that a polygon is mentioned, assume that it is a regular polygon.

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Areas of Regular Polygons

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  1. Areas of Regular Polygons Students will be able to find the areas of regular polygons.

  2. Regular Polygons • In this chapter we will be dealing only with regular polygons. Anytime that a polygon is mentioned, assume that it is a regular polygon. • The center of a regular polygon is equidistant from the vertices. • 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. Unit G

  3. Regular Polygons • In this example, point C is the center of the polygon. • a is the apothem of the polygon. • p is the perimeter of the polygon C a • The formula for the area of a regular polygon is A = ½ap Unit G

  4. The Area of an Equilateral Triangle • An equilateral triangle can be divided into two special right triangles. • In a 30-60-90 triangle, the short leg is half of the hypotenuse and the long leg is the short leg multiplied by . • The formula for the area of an equilateral triangle would be: s Unit G

  5. The Area of a Hexagon • A regular hexagon can be divided into six equilateral triangles. • So we can find the area of the regular hexagon by multiplying the area of the equilateral triangle by 6. • The formula for an equilateral triangle on the formula sheet that you can use. So just remember the 6. h b Unit G

  6. Examples of Finding Area What would be the perimeter of this regular pentagon? Use the formula A = ½ a p Find the area of each of these: 30 4.1 A = ½ • 4.1 • 30 = 61.5 6 This is a hexagon. Use the formula: 5 Unit G

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