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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 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. • 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
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
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
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
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