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.

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Presentation transcript:

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 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 triangle with the apothem. In the figure, the shorter leg would be 10, so the entire side would be 20 (same as r) 60  20

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 in 15 in

Homework p even, even