1. Chapter 8

2. 8-1 Estimating Perimeter and Area  Perimeter – total distance around the figure  Area – number of square units a figure encloses

3. 8-1 Estimating Perimeter and Area-answers  Perimeter – total distance around the figure  Area – number of square units a figure encloses 12ft ; truck cab quite tall 8 in; book is not very wide 8 in; pizza not very big 2ft ; bathtub is not very deep

4. 8-1 Estimating Perimeter and Area

5. 8-1 Estimating Perimeter and Area-answers 10 yd 12 yd 16 yd13 yd

6. 8-1 Estimating Perimeter and Area

7. 8-1 Estimating Perimeter and Area-answers about 19 cm 2 about 7 cm 2 about 10 cm 2 about 18 cm 2 ft inmi 2

8. 8-2 Area of a Parallelogram  height of a parallelogram – length of a perpendicular segment connecting base of parallelogram to the other.  Area of parallelogram: Area = bh

9. 8-2 Area of a Parallelogram

10. 8-2 Area of a Parallelogram-answers 60 m 2 25 m 2 12 ft 2 150 in 2 392 m 2

11. 8-2 Area of a Parallelogram

12. 8-2 Area of a Parallelogram-answers 3ft by 7 ft

13. 8-3 Perimeter and Area of a Triangle  base of a triangle – any side can be considered base  height of triangle – length of perpendicular segment from a vertex to the bases opposite or and extension of base Area of triangle = ½ bh or bh/2

14. 8-3 Perimeter and Area of a Triangle

15. 8-3 Perimeter and Area of a Triangle - answers 8.2 ft 23.9 in 34.6 in 416 ft

16. 8-3 Perimeter and Area of a Triangle

17. 8-3 Perimeter and Area of a Triangle-ans 299 cm 2 59.22 mi 2 26.8 km 2 1325 yd 2 4, 4, 4; 5, 5, 2

18. 8-4 Area of Other Figures  bases of trapezoid – two parallel sides of a trapezoid; b 1 and b 2  height of trapezoid – length of perpendicular segment connecting bases Area of trapezoid = ½h(b 1 + b 2 ) or h(b 1 + b 2 ) 2

19. 8-4 Area of Other Figures

20. 8-4 Area of Other Figures-answers 33 ft 2 748 ft 2 33.25 in 2 98 m 2 838 km 2 2586 yd 2

21. 8-5 Circumference and Area of a Circle Circumference – is the distance around the outside of a circle Π – the ratio of a circle’s circumference to its diameter d. Π is nonterminating and nonrepeating Π is approximate 3.14 or 22/7

22. 8-5 Circumference and Area of a Circle

23. 8-5 Circumference and Area of a Circle-answers C = Πd = Π*50 = 157.1 cm C = 2 Πr = 2*Π*40 = 251.3 in

24. 8-5 Circumference and Area of a Circle

25. 8-5 Circumference and Area of a Circle-answers C = Πd = Π*17 = 53.4 mm C = 2 Πr = 2*Π*7 = 44.0 cm

26. 8-5 Circumference and Area of a Circle

27. A = Πr 2 = Π*6 2 = 36 Π = 113 in 2 A = Πr 2 = Π*15 2 = 225 Π = 707 ft 2

28. 8-5 Circumference and Area of a Circle A = Πr 2 = Π*11 2 = 121 Π = 380 cm 2 A = Πr 2 = Π*25 2 = 625 Π = 1963 cm 2

29. 8-8 Three-Dimensional Figures  3-D figure – figure that does not lie in plane  face – flat surface of solid shaped like polygon  edge – segment formed by intersection of 2 faces  prism – 3-D figure with two parallel and congruent polygonal faces, called bases

30. 8-8 Three-Dimensional Figures Prisms are named for the shape of its bases. Name this prism.

31. 8-8 Three-Dimensional Figures Cube - rectangular prism with faces that are all squares Cylinder - bases are circles

32. 8-8 Three-Dimensional Figures Pyramids – are made up of triangular faces that meet at one point, called a vertex Cone – one base that is a circle and one vertex

33. 8-8 Three-Dimensional Figures Sphere – set of all points in space that are same distance from a center point

34. 8-8 Three-Dimensional Figures Sphere – set of all points in space that are same distance from a center point Rectangle, rectangular prism triangle, Triangular prism pentagon, Pentagonal prism

35. 8-8 Three-Dimensional Figures

36. cylinder cone sphere Hexagonal pyramid cone Rectangular pyramid

37. 8-9 Surface Area of Rectangular Prisms Net – two – dimensional pattern that you can fold into a 3-d figure

38. 8-9 Surface Area of Rectangular Prisms Net – two – dimensional pattern that you can fold into a 3-d figure Draw a net for the triangular prism. 1)First label the bases and the side. 2)Then draw the net.

39. 8-9 Surface Area of Rectangular Prisms-answers Net – two – dimensional pattern that you can fold into a 3-d figure

40. 8-9 Surface Area of Rectangular Prisms Surface Area – sum of all the area of the faces of a prism

41. 8-9 Surface Area of Rectangular Prisms-answers Surface Area – sum of all the area of the faces of a prism SA = (5+4+5+4)6 + (2*5*4) = 108 + 40 = 148 in 2 TOP = 5*4 = 20 Bottom = 5 * 4 = 20 Left = 6 * 5 = 30 Right = 6 * 5 = 30 Front = 6 *4 = 24 Back = 6 * 4 = +24 148 in 2

42. 8-9 Surface Area of Rectangular Prisms Surface Area – sum of all the area of the faces of a prism

43. 8-9 Surface Area of Rectangular Prisms Surface Area – sum of all the area of the faces of a prism SA = Ph + 2B = (7+4+7+4)6 + (2*7*4) = 132 + 56 = 188 m 2 TOP = 7*4 = 28 Bottom = 7 * 4 = 28 Left = 6 * 4 = 24 Right = 6 * 4 = 24 Front = 6 *7 = 42 Back = 6 * 7 = +42 188 m 2

44. 8-9 Surface Area of Rectangular Prisms Surface Area – sum of all the area of the faces of a prism

45. 8-9 Surface Area of Rectangular Prisms-ans Surface Area – sum of all the area of the faces of a prism SA = Ph + 2B = (1+1+1+1)2 + (2*1*1) = 8 + 2 = 10 ft 2 TOP = 1*1 = 1 Bottom = 1* 1 = 1 Left = 1 * 2 = 2 Right = 1 * 2 = 2 Front = 1 *2 = 2 Back = 1 * 2 = +2 10 ft 2

46. 8-9 Surface Area of Triangular Prisms Surface Area – sum of all the area of the faces of a prism

47. 8-9 Surface Area of Triangular Prisms-ans Surface Area – sum of all the area of the faces of a prism SA = Ph + 2B = (9+12+15)4 + 2((9*12)/2) = 144 + 108 = 252 cm 2 TOP (triangle) = 9 * 12 / 2 = 54 Bottom (triangle) = 9 * 12 / 2 = 54 Left (rectangle) = 9*4 = 36 Front (rectangle) = 15*4 = 60 Back (rectangle) = 12 * 4 = +48 252 cm 2

48. 8-9 Surface Area of Triangular Prisms Surface Area – sum of all the area of the faces of a prism

49. 8-9 Surface Area of Triangular Prisms-ans Surface Area – sum of all the area of the faces of a prism SA = Ph + 2B =(6+8+10)9 + 2((6*8)/2) = 216 + 48 = 264 m 2 Left (triangle) = 6 * 8 / 2 = 24 Right (triangle) = 6 * 8 / 2 = 24 Front (rectangle) = 9*10 = 90 Back (rectangle) = 9*6 = 54 Bottom (rectangle) = 8*9 = +72 264 m 2

50. 8-9 Surface Area of Cylinders Surface Area – sum of all the area of the faces of a prism

51. 8-9 Surface Area of Cylinders Surface Area – sum of all the area of the faces of a prism

52. 8-9 Surface Area of Cylinders-ans Surface Area – sum of all the area of the faces of a prism SA = 2 Πrh + 2Πr 2 = 2 Π10*15 + 2Π10 2 = 942 + 628 = 1570 yd 2

53. 8-9 Surface Area of Cylinders Surface Area – sum of all the area of the faces of a prism

54. 8-9 Surface Area of Cylinders-ans Surface Area – sum of all the area of the faces of a prism SA = 2 Πrh + 2Πr 2 = 2 Π5*20 + 2Π5 2 = 628 + 157 = 785 cm 2

55. 8-9 Surface Area of Cylinders Surface Area – sum of all the area of the faces of a prism

56. 8-9 Surface Area of Cylinders-ans Surface Area – sum of all the area of the faces of a prism SA = 2 Πrh + 2Πr 2 = 2 Π10*45 + 2Π10 2 = 2826 + 628 = 3454 m 2

57. 8-10 Volume of Prisms and Cylinders Volume – number of cubic units needed to fill the space INSIDE the figure Cubic unit – a cube with edges one unit long

58. 8-10 Volume of Prisms and Cylinders

59. Volume of a Rectangular Prism V = Bh = area of base * height = l * w * h

60. 8-10 Volume of Prisms and Cylinders

61. 8-10 Volume of Prisms and Cylinders-answers V = Bh = l * w * h = 20 * 7 * 8 = 1120 in 3 V = Bh = l * w * h = 8 * 10 * 8 = 640 ft 3

62. 8-10 Volume of Prisms and Cylinders

63. 8-10 Volume of Prisms and Cylinders-ans V = Bh = b*h * h 2 = 6*6* 8 2 = 192 cm 3 V = Bh = b*h * h 2 = 3*4* 5 2 = 30 in 3

64. 8-10 Volume of Prisms and Cylinders

65. 8-10 Volume of Prisms and Cylinders-ans V = Bh = b*h * h 2 = 12*28* 10 2 = 1680 m 3

66. 8-10 Volume of Prisms and Cylinders Find the height of each rectangular prism given the volume, length, and width. V = 3375 m 3 V = 900 ft 3 L = 15 m L= 45 ft W = 15 m W = 2 ft H = ?

67. 8-10 Volume of Prisms and Cylinders-ans Find the height of each rectangular prism given the volume, length, and width. V = 3375 m 3 V = 900 ft 3 L = 15 m L= 45 ft W = 15 m W = 2 ft H = ? 15 m H = ? 10 ft

68. 8-10 Volume of Prisms and Cylinders

69. 8-10 Volume of Prisms and Cylinders-ans V = Bh = Πr 2 * h = Π 1 2 * 10 = 31 ft 3 V = Bh = Πr 2 * h = Π 14 2 * 80 = 49260 m 3

70. 8-10 Volume of Prisms and Cylinders

71. 8-10 Volume of Prisms and Cylinders-ans V = Bh = Πr 2 * h = Π 6 2 * 18 = 2036 in 3