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D. Area and Surface Area

D. Area and Surface Area. Math 10: A and W. Key Terms :. Find the definition of each of the following terms: Area Surface Area Geometric Net Perimeter Scale Factor. 1. Area Review.

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D. Area and Surface Area

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  1. D. Area and Surface Area Math 10: A and W

  2. Key Terms: • Find the definition of each of the following terms: • Area • Surface Area • Geometric Net • Perimeter • Scale Factor

  3. 1. Area Review • You have looked at the area of 2D shapes before so we are going to do a quick review of some of the common shapes you will see and would see in the work force.

  4. Triangle • Example

  5. Why do we measure Area in ? • Because that is what area is…how many squares of a certain size (ex. square inch) fill up a 2D shape

  6. b) Rectangle • Example

  7. c) Parallelogram – is a quadrilateral with 2 pairs of parallel sides a = amplitude • Example

  8. d) Trapezoid – is a quad with only 2 parallel sides • Example

  9. e) Rhombus – a parallelogram with 4 congruent sides • Example

  10. f) Circle r = radius • Example

  11. g) Unusual Shapes • To find the area of an unusual shape, add line segments to divide the shape into smaller known shapes. Then add the area of all the smaller shapes to get the area of the whole shape. • Examples

  12. Building your Skills • Handout

  13. 2. Area in SI and Imperial Measures • In many jobs you don’t simply have to calculate area but also have to convert between measurement systems. • Also it is the case in most jobs that calculating area is done for the purpose of knowing how much material is needed and therefore how much the project will cost.

  14. Example • Tiff would like to replace the carpet in her living room. She used her imperial tape measure to measure the room, and the dimensions were 12’ by 15’. When she went to the carpet store, she found that the price of the carpet was $24.99/ (tax included). She cannot order less than full square meter of carpet. • How much carpet does she need? • How much will the carpet cost?

  15. Example • Sean is the cost estimator for a landscape company. He has to calculate the amount of material needed to construct a circular outdoor patio built from paving stones. The diameter of the patio is 13m. One bundle of paving stones covers 116. Sean has ordered 11 bundles of paving stones. Did her order enough paving stones.

  16. Activity 3.5 – Designing a CFL Field Logo p. 110 • We will read through together and then with partners you can work through the activity so that we are doing it properly.

  17. Discuss the Ideas – Lake Winnipeg p. 111 • Read through together and solve

  18. Area Units and Conversion

  19. Building your Skills • Ex. 3.2 (p. 111) 1-8, 9 for extra challenge

  20. 3. Surface Area • Math on the Job p. 115 • Read through together and solve

  21. Have you ever noticed the many types of packaging used to contain goods? • Cereal, detergent, and tissue are sold in rectangular boxes. Soup and tuna come in a cylindrical can.

  22. In order to know how much packaging material is required for a product, its surface area must be calculated. • Trades people such as machinists also need to calculate surface are to determine the amount of material they need to fabricate parts.

  23. One way to find the surface area of a 3D object is to create a geometric net. • A geometric net is created by imagining that you are cutting open a 3D object and laying it out flat to create a 2D figure. The surface area can then be found by summing the areas of each side, or face, of the 2D net.

  24. To find the perimeter of an enlargement or reduction, multiply the scale factor by the original perimeter. • To find the area of an enlargement or reduction, multiply the square of the scale factor by the original area (A x )

  25. Discuss the Ideas – Scale Factor p. 116 • We will read through together and solve

  26. Activity 3.7 – Surface Area Formulas • You will work in partners for this activity. • You and your partner will need one set of the geometric nets • We will read through together before you start

  27. Activity 3.6 – Designing a tool box p. 116 • Work through with a partner

  28. Example • A cannery has redesigned the size of the can for its canned salmon. The diameter of the new can is 4” and its height is 5.5”. How much tin will be needed to construct one can?

  29. Example • Logan manufactures and sells farm implements. One piece of equipment that he sells is a 3-point spreader that attaches to a tractor to spread grass seed, wheat seed, etc. The hopper of the spreader is a cone with a diameter of 40” and slant height of 45”. How many square feet of plastic is needed to form one hopper?

  30. So to convert Area or Surface Area you have to square the conversion factor you are going to use before multiplying. • That is different from scale factor which has to do with changing size and conversion factors change the units not size. • Let’s go back to the last two examples and convert the answers using a squared conversion factor.

  31. Activity 3.8 – A Redecorating Project p. 120 • We will read through and solve together.

  32. Mental Example • The surface area of a cube is 24 Find the area of one face and the length of one side of the cube.

  33. Building Your Skills • Ex. 3.3 (p. 121) #1-6, 7 challenge

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