Scalene Triangle Answer Key

ху 1 1 ог - ху· 6.AFP: - ог - ху· 6.AFK: 12' 12 ' 16 ' ху 1 ху 1 - ог -ху· 6.КРМ: - ог - ху· 8 ' 48' 48 ' 8' ху ху 1 6.РFМ: - ог - ху· 6.AKD: - ог 24' 24 ' 8' ху ху ог -1ху· 6.ASD: -1ху· 6.AMD: 8 ' 4 ' 4' 6' ху 1 1 ог - ху· 6.AHD: - ог - ху· 6.AMS: 4' 6 ' 4 ' ху 1 ху 1 - ог - ху· 6.АМН: - ог - ху· 12' 12 ' 8 ' 8' ху ог -1ху· 6.ARH: ху 6.АВМ: - ог 4 ' 4' 6' 1 ху 1 ху -ху· 6.АСН: - ог -ху· 6.ACD: 4' 4 ' 6 ' 2' 1 ху 1 ог - ху; 6.АВН: - , ог -ху 2 2 2 Practice В 1. PossiЫe answer: А "' 30 ft2 2. А "' 28.3 ft2 4. 3. А "' 30 units 2 у kite; Р"' 15.2 units; А= 12 units 2 у 5. s х • ➔ R ProЫem Solving 1. 128.6cm 2 2. $13.80 3. А 4. G 5. С 6. Н р trapezoid; Р"' 20.3 units; А= 21 units 2 6. Reading Strategies 2. А"' 62.8in 2 1. А= 9cm 2 у F 3. А= 109m2 LESSON 9-4 Practice А 1. А"' 19 yd 2 3. G 2. А"' 22.5 units 2 scalene triangle; Р"' 15.2 units; А = 7 units 2 у 7. у х С("""1, -2) 4. ✓10 ; ✓10 ; ✓10 ; ✓10 5. а square 6. 1О units 2 7. 4 units 8. А= 16 units 2 9. А = 6 units 2 10. А= 10 units 2 ✓10 11. А= 14 units 2 rectangle; Р= 14.1 units; А= 12 units 2 6. The perimeter is douЫed. The агеа is multiplied Ьу 4. Challenge 1. А== 0.063 units 2 2. about 32 3. Answers will vary: == 2 Practice В 4. about 16 5. Answers will vary: == 1 1. The агеа is multiplied Ьу �4 6. Answers will vary: == О 2. The агеа is divided Ьу 6. 3. The агеа is douЫed. ProЫem Solving 1. Р == 22.8 units; А = 28 units2 4. The агеа is multiplied Ьу 2 2. Р == 12.1 units; А = 4 units 3. А= 31.5 units2 5. The perimeter is multiplied Ьу 2 4. PossiЫe answer: А == 36 m 5. С !. 3 агеа is multiplied Ьу 6. F 7. D 20.. 9 .i.3 The 6. The perimeter is tripled. The агеа is multiplied Ьу 9. Reading Strategies 7. The perimeter is divided Ьу 2. The агеа is divided Ьу 4. 1. 8. The perimeter is multiplied Ьу 1 агеа is multiplied Ьу - - . 64 !. 8 The ✓5. 1 О. The circumference is divided Ьу ✓2 . 9. Both diagonals аге multiplied Ьу 2. Draw а rectangle around the polygon. 3. Each side of the polygon should Ье horizontal ог vertical through а vertex. Practice С 1. PossiЫe answer: The formula for the агеа of а rectangle is А = .ew, where f is the length and w is the width of the rectangle. The initial агеа is Л = .ew. 4. 32 units2 LESSON 9-5 Multiplying either f or w Ьу n gives А с = nfw. Therefore А с = nAi. Practice А 1. The агеа is tripled. 2. The агеа is multiplied Ьу 3.. 3 3. The агеа is multiplied Ьу !5 . 4. The circumference is multiplied Ьу 1 The агеа is multiplied Ьу - . 16 2. PossiЫe answer: The formula for the агеа of а triangle is А= !ьh, where Ь is 2 the length of the base and h is the height. !4 . 5. The perimeter is multiplied Ьу 8. The агеа is multiplied Ьу 64. The initial агеа is Ai = !ьh. Multiplying Ь 2 Ьу n and h Ьу n gives А с = !2 bnhn, ог А 2 = !n2 bh. Therefore Ас = n A 2 с Practice В 5 12 2. 7 12 3. 1 4. 2 3 5. 1 3 6. 1 9 7. 59 72 8. 35 72 1. 9. 0.21 1о. 0.20 11. 0.41 12. 0.59 7. 11 24 1 8. _ 12 9. 0.14 10. 0.16 11. 0.57 12 .0.34 Challenge 1. а. у PossiЫe answers based оп an 11.5 yd2 estimate for the green: 13. 0.019 14. 0.001 15. 937 shots 16. 0.425 { О s xs Б О s у..; Б Ь. 36 square units 2. а. Practice С 1. 1 .30 х 10-4 2. 199 days 17 hours 2 minutes о 3. 0.59 OsxsБ {OsysБ 4. 1 minute 49 seconds 5. PossiЫe answer: А whole circle contains 360 ° , and its агеа is п?. А half circle contains 180 ° , and its агеа is half of а whole circle, ог п?. Therefore the агеа of the half circle divided Ьу the агеа of the whole circle is , which is equal to the angle measure of the half circle (180 ° ) divided Ьу the angle measure of the whole circle (360 ° ). So the angle measure of а region of а circle divided Ьу 360 ° equals the ratio of their areas, which is the geometric probaЬility. 6. 0.15 Ь. 8 square units 3. а. 8 2 , or 36 9 Ь. � 1 4. а. 18 Ь. ?_ 8 с. 1, ог 100% d.O 7. 33 minutes 51 seconds 1 5. а. 8 Reteach 1. 3 8 2. 3 8 ь. 28 3. 7 8 4. 3 4 С. - 5. 3 8 6. 5 24 1 4 Performance Assessment CHAPTER9 1. а. 1.96 Ь. PossiЫe answer: 25 - 1.96 = 23.04; RQ2 = (23.04)(25); RQ = 24 Section Quiz: Lessons 9-1 Through 9-3 1. С 7. А с. PossiЫe answer: Qs2 = (23.04 )(1.96); QS=6.72 2. F 8. G 3. А 9. D d. .2_ 24 4. Н 10. F 5. D 11. А 6. Н 12. G е. 16 ° 2. a. 152 =62 +162 -2(6)(16)cosK ь. 70 3_ а. Section Quiz: Lessons 9-4 Through 9-6 ° sin(180 -(85 + 70))0 LK ь. 5.4 sin 70 ° 12 4. Law of Sines; the given information includes two angles and опе side. The Law of Cosines requires knowing either two sides and ап angle ог all three sides. The Law of Sines requires knowing а mix of both sides and angles. Cumulative Test в 1. D 17. 2. G 18. J 33. 3. D 19. А 4. G 20. н 34. G 35. D 5. В 21. А 36. G 6. F 22. G 37. 7. С 23. 38. G 8. J 24. 9. В 25. с н с 32. J с в 39. D 40. н 10. Н 26. F 41. А 11. А 27. D 42. 12. Н 28. 43. 13. В 29. D 44. 14. F 30. J 45. 15. С 31. А 46. J 16. F н н в н с 1. В 6. G 2. Н 7. В 3. D 8. G 4. F 9. В 5. С Chapter Test Form А: Multiple Choice 1. А 10. А 2. В 11. В 3. С 12. D 4. В 13. С 5. С 14. А 6. В 15. А 7. В 16. А 8. С 17. В 9. С 18. В Chapter Test Form В: Multiple Choice 1. А 10. G 2. F 11. С 3. D 12. G 4. G 13. D 5. В 14. G 6. G 15. С 7. В 16. G 8. F 17. В 9. В 18. Н Chapter Test Form С: Multiple Choice 12. 10 units 13. 9 units2 14. 12 units2 15. The circumference is multiplied Ьу 2. 16. PossiЫe answers: douЫe the width; douЫe the length. 17. 2 9 18. 2 ог 0.5 1 Chapter Test Form В: Free Response 1. 60 cm2 2. 264 cm2 1. С 10. F 2. Н 11. D 3. В 12. Н 4. 7ft 5. 168 cm2 4. Н 13. В 6. 96 in2 5. В 14. G 7. 18 cm 6. Н 15. D 8. 201.06 cm2 7. С 16. Н 8. Н 17. В 9. В 18. G Chapter Test Form А: Free Response 1. 54 cm2 3. 216 cm2 9. 259.8 cm2 1О. 36.53 in2 1 11. Ассер! answers between 16-yd 2 and 2 18 yd 2. 5 12. 10 ✓ units 13. 12 units2 2. 66 cm2 14. 106.8 units2 3. 108 in2 4. 144 cm2 5. 40 in2 6. 49 in2 7. 61t cm 2 8. 161t cm 9. 61.9 cm2 10. 432 cm 2 11. about 3 in2 15. The агеа is multiplied Ьу 9. 16. 4 ft 17. 1 8 18. 8 15 Chapter Test Form С: Free Response 2 3 1 �✓ • 4 2. 24.27 cm2 3 3. 18✓ in2 4. 138 cm2 3 5. 64✓ mm2 ог about 110.85 mm2 Ь. The агеа of the half circle • IS 6. 36 cm 2 7. 8п✓ in. is 6 х 1.5 cm and the apothem 5 а is \ .Jз cm. The агеа of the 10. 54.4 cm2 11. PossiЫe answer: $47.00 hexagon alone is i(\ 13. 106.8 units 2 14. 29 units2 15. The original агеа is multiplied Ьу 18. 16. (25пх" + 1ООпх + 1 ООп) ft2 3 4 2 hexagon is iaP where the perimeter 9. 128 cm2 17. 1.5 1С ( cm , w h'ICh •IS 2 2 ) 2•25п 2 cm = 0.88 cm2 . The агеа of the 8. 280.6 ft2 12. 17.2 units 1 ог0.75 18. опсе Performance Assessment 1. а. PossiЫe answer: 5 3 ✓ }6х1.5) = 5.85 cm2 . The total агеа = 6.73 cm2 !о the nearest hundredth. 3. а. Draw а rectangle around it so that the vertices lie оп different sides of the rectangle. Find the агеа of the rectangle and suьtract the triangle areas. Ь. 72 units2 с. 648 uni!s2 Cumulative Test 1. D Ь. PossiЫe answer: Both heights аге 8 units. The ratio of the агеа of the triangle !о that of the rectangle is ib(8) 1 (16)(8) 4 Solving for Ь renders Ь = 8. 1 с. 4 1 2. а. 1 would use А =-аР !о find the агеа 2 1 of the regular hexagon and А= -nr2 2 to find the агеа of the half circle. Then I would add the two areas. 31. 18. F 33. D 2. G 17. D 4. G 19. 6. F 21. 3. D 5. А 7. А 8. Н 9. В 10. J 20. с н 22. н 23. D 24. G 34. F 35. с 37. с н 36. F 38. 39. А 40. G 27. А 42. F 26. 13. В 28. 15. А 30. 14. G 32. в н 25. 11. С 12. G с н 16. Н 29. н в н 41. в 43. с 44. F