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Comprehensive Guide to Measurement, Ratios, and Three-Dimensional Geometry

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This chapter explores crucial concepts in measurement, including ratios, units, and tools for precise calculations such as compasses, protractors, and scales. It defines perimeter, circumference, and area for various shapes, while also discussing probability and problem-solving techniques for irregular shapes. Additionally, it covers three-dimensional figures like polyhedrons, prisms, pyramids, cylinders, cones, and spheres, detailing their properties and surface areas, along with formulas for calculation. This is an essential resource for understanding measurements in geometry.

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Comprehensive Guide to Measurement, Ratios, and Three-Dimensional Geometry

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  1. CHAPTER 5 MEASUREMENT

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

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

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

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