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

Unit G2 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 apothem is the distance from the center to a side. A central angle of a regular polygon has its vertex at the center and its sides pass through consecutive vertices.

Unit G3 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 The formula for the area of a regular polygon is A = ½ap a C

Unit G4 The Area of an Equilateral Triangle An equilateral triangle can be divided into two special right triangles. In a triangle, the short leg is half of the hypotenuse and the long leg is the short leg multiplied by. s The formula for the area of an equilateral triangle would be:

Unit G5 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. b h The formula for an equilateral triangle on the formula sheet that you can use. So just remember the 6.

Unit G6 Examples of Finding Area Find the area of each of these: What would be the perimeter of this regular pentagon? Use the formula A = ½ a p 30 5 This is a hexagon. Use the formula: A = ½ = 61.5