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Area of circles, sectors and arc lengths

Area of circles, sectors and arc lengths. Area Unit Day 4 Tuesday January 6, 2009. Warm Up. HW Answers p. 443 1-4. Square. 1. a = 8; A = 256 2. r = ; A = 100 3. r = ; a = 7/2 4. r = ; A = 24. r. a. ½ side. 45-45-90  radius = hypotenuse

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Area of circles, sectors and arc lengths

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  1. Area of circles, sectors and arc lengths Area Unit Day 4 Tuesday January 6, 2009

  2. Warm Up

  3. HW Answers p. 443 1-4 Square • 1. a = 8; A = 256 • 2. r = ; A = 100 • 3. r = ; a = 7/2 • 4. r = ; A = 24 r a ½ side 45-45-90  radius = hypotenuse apothem = leg ½ side = leg = apothem

  4. HW Answers p. 443 5-8 Equilateral  5. a = 3; p = ; A = 6. r = 8; p= ; A = 7. r = ; a = ; A = 8. r=3; a=3/2; A = r a 60° 30° ½ side 30-60-90  radius = hypotenuse apothem = shorter leg ½ side = longer leg

  5. HW Answers p. 443 9-12 Hexagon Each interior = 120° 9. a = ; p = 24; A = 10. r = 10; p=60; A = 11. r = ; a = ; A = 12. r = ; a = 3; A = 120° r a 60° ½ side 30-60-90  radius = hypotenuse apothem = longer leg ½ side = shorter leg

  6. HW Answers p. 443 13, 14 Hexagon Each interior = 120° 13. a = ;s = 12; p = 36 r a 30° 60° 30° ½ side 45° 6 14.

  7. HW Answers p. 443 15-17 15. 16. 17. a) b) .3090 c) 6.18 d) .2939 e) 2.939

  8. Area of a circle A = r2 r

  9. Sector Sector of a circle is the region bounded by two radii and an arc of the circle. Sector AOB r O A r B

  10. Area of a Sector AOB is a central angle. Sector AOB is a fraction or part of the whole circle’s area r What fraction or part of the circle is sector AOB? O A r B

  11. Area of a Sector AOB = 90° Sector AOB is or of circle O O r A r B

  12. Area of a Sector AOB = 90° Sector AOB is or of circle O Area of sector AOB = O A ¼ the area of circle O or 6 B

  13. Area of a Sector formula Area of sector AOB = O A r B

  14. circumference of a circle C = 2r or d Circumference measures the length of the outside arc or edge of the circle r

  15. Arc length Arc Length – a piece of the edge of a circle or a fraction of the circumference.

  16. Arc length Arc Length =

  17. Example 1 • Find the area of a sector that has a 40° central angle and a radius of 20 m. O 20 m A 40° B

  18. Example 2 • Find the area of the shaded region in circle O. O 10 m A 120° B

  19. homework P. 448 2-12 even, 16 and 26 and P. 453 2-16 even Quiz tomorrow on areas of polygons – you will have the area formulas

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