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Geometry

Geometry. 12.1 Prisms. Prisms. Today you will learn how to find three measurements about prisms. You will find:. Some new vocab list words…. Lateral area: L.A. Total area: T.A. Volume: V. Different Prisms. Lateral faces are not rectangles.

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Geometry

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  1. Geometry 12.1 Prisms

  2. Prisms Today you will learn how to find three measurements about prisms. You will find: Some new vocab list words… Lateral area: L.A. Total area: T.A. Volume: V

  3. Different Prisms Lateral faces are not rectangles lateral faces are rectangles Right rectangular prism Right hexagonal prism Oblique triangular prism

  4. Prism Vocabulary base shaded faces lie in parallel planes congruent polygons base lateral faces faces(not bases) ecaf parallelograms that intersect each other in lateral edges ecaf face face base lateral edges

  5. Prism Vocabulary altitude segment that joins the two bases. It is perpendicular to both. In a right prism,the lateral edges are altitudes back right side left side front height the length of an altitude referred to as H lateral area sum of the areas of the lateral faces + + +

  6. To find lateral area (L.A.): Find the perimeter of the base Multiply it by height Imagine a curtain around the base, then raising it up. H H H H H + + + width length width length = PERIMETER To find total area (T.A.): Add the lateral area (L.A.) With the area of the 2 bases width width length length

  7. Lateral Area of a Prism: L.A. The lateral area of a right prism equals the perimeter of a base times the height of the prism. L.A = pH 8 4 6 LA = [2(6) +2(4)] • 8 = 160 square units

  8. Total Area of a Prism: T.A. The total area of a right prism equals the lateral area plus the areas of both bases. T.A = L.A. + 2B 8 4 6 LA = 160 + 2(6 • 4) = 160 + 48 = 208 square units

  9. 20 9 cm 5 4 cm 12 9 cm Exercises Find the (a) lateral area and (b) total area of each right prism. base = ½(5)(12) base = 9(4) 2. (a) 1. (a) LA = pH LA = pH LA = [5 + 12 + 13] (20) LA = [2(9) + 2(4)] (9) LA = 600 LA = 234 cm² (b) TA = LA + 2B (b) TA = LA + 2B TA = 600 + 2[(½)(5)(12)] TA = 234 + 2(36) TA = 660 TA = 306 cm²

  10. 10 cm 13 cm 13 cm 20 cm 20 cm Exercises Find the (a) lateral area and (b) total area of each right prism. 3. (a) LA = pH LA = (56)(20) H = 20 LA = 1120 cm² (b) TA = LA + 2B Base is a trapezoid TA = 1120 + 2(180) 10 TA = 1480 cm² P = 10 + 20 + 13 + 13 13 13 12 = 56 A = hm 5 5 20 A = 12•15 = 180

  11. To find volume (V): Find the area of the base Multiply it by height H width length

  12. Volume of a Prism: V The volume of a right prism equals the area of a base times the height of the prism. V = BH 8 4 6 V = (6 • 4) • 8 = 192 cubic units

  13. Exercises 12 12 h 900 144 336 w 1900 208 576 432 l 5000 192 720 TA = LA + 2B 9. 216 = 4p p = 54 10. V = BH 576 = 48H H = 12 LA = pH = 216 + 2(15•12) = [2(8) + 2(6)] • 12 = 216 + 360 54 = 2(15) + 2w = 336 = 576 TA = LA + 2B 2w = 24 V = BH = (15•12) • 4 = 720 = 336 + 2(8•6) = 336 + 96 = 432 w = 12

  14. Homework • pg. 477 CE #1-10 • WE #1-25 odd

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