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Warm Up 1. Find w , y , and z . Give the answers in simplest radical form.

Warm Up 1. Find w , y , and z . Give the answers in simplest radical form. 2. RT. Warm Up Continued Find each measure. 54. 3. UQ. 11-3. Sector Area and Arc Length. Holt Geometry. Example 1A: Finding the Area of a Sector.

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Warm Up 1. Find w , y , and z . Give the answers in simplest radical form.

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  1. Warm Up 1.Find w, y, and z. Give the answers in simplest radical form.

  2. 2. RT Warm Up Continued Find each measure. 54 3. UQ

  3. 11-3 Sector Area and Arc Length Holt Geometry

  4. Example 1A: Finding the Area of a Sector Find the area of each sector. Give answers in terms of and rounded to the nearest hundredth. sector HGJ Use formula for area of sector. Substitute 12 for r and 131 for m. Simplify. = 52.4 m2  164.62 m2

  5. A segment of a circle is a region bounded by an arc and its chord.

  6. Example 3: Finding the Area of a Segment Find the area of segment LNM to the nearest hundredth. Step 1 Find the area of sector LNM. Use formula for area of sector. Substitute 9 for r and 120 for m. Simplify. = 27 cm2

  7. Step 2 Find the area of ∆LNM. Draw altitude NO. Example 3 Continued Find the area of segment LNM to the nearest hundredth. Simplify.

  8. Remember! In a 30°-60°-90° triangle, the length of the leg opposite the 60° angle is √3 times the length of the shorter leg.

  9. Example 3 Continued Find the area of segment LNM to the nearest hundredth. Step 3 area of segment = area of sector LNM – area of ∆LNM  49.75 cm2

  10. Check It Out! Example 3 Find the area of segment RST to the nearest hundredth. Step 1 Find the area of sector RST. Use formula for area of sector. Substitute 4 for r and 90 for m. Simplify. = 4 m2

  11. Check It Out! Example 3 Continued Find the area of segment RST to the nearest hundredth. Step 2 Find the area of ∆RST. ST = 4 m, and RS = 4m. = 8 m2 Simplify.

  12. Check It Out! Example 3 Continued Find the area of segment RST to the nearest hundredth. Step 3 area of segment = area of sector RST – area of ∆RST = 4 – 8  4.57 m2

  13. Example 4A: Finding Arc Length Find each arc length. Give answers in terms of  and rounded to the nearest hundredth. FG Use formula for area of sector. Substitute 8 for r and 134 for m.  5.96 cm  18.71 cm Simplify.

  14. Lesson Quiz: Part I Find each measure. Give answers in terms of and rounded to the nearest hundredth. 1. area of sector LQM 7.5in223.56 in2 2. length of NP 2.5 in. 7.85 in.

  15. Lesson Quiz: Part II 3. The gear of a grandfather clock has a radius of 3 in. To the nearest tenth of an inch, what distance does the gear cover when it rotates through an angle of 88°? 4.6 in. 4. Find the area of segment GHJ to the nearest hundredth. 55.94 m2

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