11.3 Areas of Regular Polygons and Circles Objectives: Find areas of regular polygons and circles.

apothem (of a polygon) Apothem = line segment from center of polygon that is perpendicular bisector of a side of the polygon Apothem = a a

area of a regular polygon Regular polygon = all sides are equal Areareg polygon = ½ Pa, P = perimeter of polygon a = apothem a 12 in.

Find the area of a regular hexagon with a perimeter of 72 in. Areareg polygon = ½ Pa, P = perimeter of polygon a = apothem P = 72 in., a = ? a = 63 A = ½ (72)(63 )  374.1 in2 a

Find the area of a regular octagon with a perimeter of 80 in. Areareg polygon = ½ Pa, P = perimeter of polygon a = apothem P = 80 in., a = ? Tan 22.5 = 5/a a = 5 / tan 22.5 = 12.07 A = ½ (80)(12.07 )  482.8 in2 22.5° a 5 in.

Find the area of a regular triangle with apothem length of 30 in. Areareg polygon = ½ Pa, P = perimeter of polygon a = apothem P = 6x, a = 30 in. tan 60 = x / 30 x = 30 tan 60 = 51.96 P = 311.77 A = ½ (311.77)(30 )  4676.5 in2 60° 30 x