1. CHAPTER 5
MEASUREMENT

2. Ratios and Units of Measure
SECTION 5-1
Ratios and Units of Measure

3. MEASUREMENT– is a process used to find size, quantities, or amounts

4. COMPASS – is used for drawing curved lines and circles for measuring distances.

5. PROTRACTOR – is an instrument for measuring and drawing angles.

6. SCALES or RULERS – devices for measuring distance.

7. CALIPERS and MICROMETERS – devices used for making precise measurements

8. PRECISION – is related to the unit of measure used.

9. GREATEST POSSIBLE ERROR – is ½ the smallest unit used to make the measurement.

10. RATIO – is a quotient of two numbers that compares one number with the other.

11. RATE – is a ratio that compares two different quantities

12. UNIT RATE – compares a quantity to one unit of that quantity

13. Perimeter, Circumference and Area
SECTION 5-2
Perimeter, Circumference and Area

14. PERIMETER – is the distance around a polygon.

15. CIRCUMFERENCE – is the distance around a circle.

16. AREA – the amount of surface a figure covers.

17. Circle
C = d or 2r
A =r2

18. Rectangle or Square
P = 2l + 2w
A = lw

19. Triangle
A = ½bh

20. Parallelogram
A = bh

21. Trapezoid
A = ½h(b1+b2)

22. SECTION 5-3
Probability and Area

23. PROBABILITY – the likelihood that an event will occur.

24. number of favorable outcomes ÷ number of possible outcomes
P(any event) =
number of favorable outcomes ÷ number of possible outcomes

25. Problem Solving Skills: Irregular Shapes
SECTION 5-4
Problem Solving Skills: Irregular Shapes

26. Three-dimensional Figures and Loci
SECTION 5-5
Three-dimensional Figures and Loci

27. POLYHEDRON– is a three-dimensional figure in which each surface is a polygon and

28. The surfaces are called faces
The surfaces are called faces. Two faces intersect at an edge, and a vertex is a point where three or more edges intersect.

29. PRISM - a polyhedron with two identical parallel faces
PRISM - a polyhedron with two identical parallel faces. Each of these faces is called a base and

30. a prism is named by the shape of its bases.

31. PYRAMID - a polyhedron with only one base
PYRAMID - a polyhedron with only one base. The other faces are triangles that meet at a vertex and

32. a pyramid is named by the shape of its base.

33. LATERAL FACES - are those faces that are not bases.

34. LATERAL EDGES - are the edges of lateral faces and can be parallel, intersecting,or skew.

35. CYLINDER - a three-dimensional figure having a curved region with two parallel congruent circular bases. Its axis joins the centers of the two bases.

36. CONE - a three-dimensional figure having a curved surface and one circular base. Its axis is a segment from the vertex to the center of the base.

37. SPHERE - is the set of points in space that are the same distance from a given point called the center of the sphere.

38. Surface Area of Three-dimensional Figures
SECTION 5-6
Surface Area of Three-dimensional Figures

39. SURFACE AREA - The sum of the areas of all the faces of a three-dimensional figure.

40. FORMULAS

41. Square base
A = s2

42. Square prism
SA = 6s2

43. Rectangular Prism
SA = 2(lw + lh + wh)

44. Triangular face
A = ½bh

45. Circular base
A = r2

46. Curved surface
A = 2rh

47. Cylinder
SA = 2rh + 2r2

48. Cone
SA = rs + r2
S is the slant height

49. Sphere
SA = 4r2

50. Volume of Three-dimensional Figures
SECTION 5-7
Volume of Three-dimensional Figures

51. FORMULAS

52. where B = area of the given base
Prism
V = Bh
where B = area of the given base

53. where B = area of the given base
Pyramid
V = 1/3Bh
where B = area of the given base

54. Cylinder
V = r2h

55. Cone
V = 1/3r2h

56. Sphere
V = 4/3r3

57. END