11 3 Areas of Regular Polygons and Circles

11. 3 Areas of Regular Polygons and Circles What you’ll learn: 1. To find areas of regular polygons. 2. To find areas of circles.

Area of a Circle A=πr² This is not the same as C=2πr because squaring and multiplying by 2 are not the same operation!

Area of a Regular Polygon Parts of a regular polygon radius – drawn from the center of the polygon to a vertex. The radius bisects the angle it is drawn to. (number of radii=number of sides) perimeter – sum of the measures of the sides apothem – segment drawn from the center to a side. It bisects the sides and is perpendicular to that side. (number of apothems=number of sides) If a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, then A=½Pa.

Hints 20 In a regular polygon, the apothem and radius form a right triangle. This means that all information about right triangle applies. (Pythagorean thm. , special right triangles, trig ratios) In a regular HEXAGON, (any only a regular hexagon) the length of the radius is the same as the length of a side. Why is this? Because each angle is 120, when the radius is drawn, it creates a 30 -60 -90 triangle with the apothem. In the figure, the shorter leg 60 would be 10, so the entire side would be 20 (same as r)

Find the area of each polygon. Round to the nearest tenth. Find the area of a regular pentagon with a perimeter of 90 meters. Find the area of a regular hexagon with an apothem length of 30 in.

Find the area of each shaded region. 1. 2. 8 i n 15 in

Homework p. 613 8 -22 even, 40 -44 even