Warm - up Find the area of each figure. 1.A square with sides 12 in. 2.An equilateral triangle with sides 5 cm. 1.144 in 2 2.  10.8 cm 2.

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Presentation transcript:

Warm - up Find the area of each figure. 1.A square with sides 12 in. 2.An equilateral triangle with sides 5 cm in 2 2.  10.8 cm 2

Areas of Circles and Sectors Section 6.8

Standards MM2G3. Students will understand the properties of circles.MM2G3. Students will understand the properties of circles. –c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector. –d. Justify measurements and relationships in circles using geometric and algebraic properties.

Essential Questions Unit: What measurements can I make on curved shapes?Unit: What measurements can I make on curved shapes? Lesson:Lesson: –What are the important circle measurements?

Theorem: Area of a Circle The area of a circle is  times the square of the radius or A =  r 2.The area of a circle is  times the square of the radius or A =  r 2.

Example 1 A =  r 2 A =  (8) 2 A = 64  in 2 A  in 2

Try This! Find the area of the circle with the given information.Find the area of the circle with the given information. a.Radius 3 m b.Diameter 18 ft a. A  m 2 b. A  ft 2

Definition sector of a circle – the region bounded by two radii of the circle and their intercepted arc.sector of a circle – the region bounded by two radii of the circle and their intercepted arc.

Theorem: Area of a Sector The ratio of the area A of a sector of a circle to the area of the circle is equal to the ratio of the measure of the intercepted arc to 360º.The ratio of the area A of a sector of a circle to the area of the circle is equal to the ratio of the measure of the intercepted arc to 360º.

Example 2 Find the area of the sector shown.Find the area of the sector shown. A  ft 2

Try This! Find the area of the sector shown.Find the area of the sector shown. A  m 2

Example 3 Find the areas of the sectors formed by  ACB.Find the areas of the sectors formed by  ACB.

Summarizer Describe how to find the area of a sector of a circle.Describe how to find the area of a sector of a circle.

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