Geometry 12 1 Prisms Prisms Some new vocab

Geometry 12. 1 Prisms

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

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

Prism Vocabulary shaded faces lie in parallel planes congruent polygons faces (not bases) parallelograms that intersect each other in lateral edges ecaf af lateral faces base ec base face base c fa e

Prism Vocabulary altitude segment that joins the two bases. It is perpendicular to both. In a right prism, the lateral edges are altitudes height the length of an altitude referred to as H lateral area sum of the areas of the lateral faces + + + back t f e l e front d i s ht g ri e sid

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 width H + H length + width H + length = PERIMETER To find total area (T. A. ): Add the lateral area (L. A. ) dt h length wid t h With the area of the 2 bases

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 = p. H 8 6 4 LA = [2(6) +2(4)] • 8 = 160 square units

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. + 2 B 8 6 4 LA = 160 + 2(6 • 4) = 160 + 48 = 208 square units

Exercises Find the (a) lateral area and (b) total area of each right prism. 9 cm 4 cm base = 9(4) 1. (a) LA = p. H LA = [2(9) + 2(4)] (9) LA = 234 cm² (b) TA = LA + 2 B 5 12 2 0 base = ½(5)(12) 2. (a) LA = p. H LA = [5 + 12 + 13] (20) LA = 600 (b) TA = LA + 2 B TA = 234 + 2(36) TA = 600 + 2[(½)(5)(12)] TA = 306 cm² TA = 660

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

To find volume (V): Find the area of the base Multiply it by height H length w th d i

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 6 4 V = (6 • 4) • 8 = 192 cubic units

Exercises 7. 8. 9. 10. l 25 8 15 8 w 20 4 H 10 6 L. A. T. A. V 900 1900 5000 12 6 4 12 216 144 336 208 192 576 432 720 h l w 576 TA = LA + 2 B 9. 216 = 4 p = 216 + 2(15 • 12) p = 54 = 216 + 360 54 = 2(15) + 2 w = 576 2 w = 24 V = BH = (15 • 12) • 4 = 720 w = 12 10. V = BH LA = p. H = [2(8) + 2(6)] • 12 = 336 576 = 48 H H = 12 TA = LA + 2 B = 336 + 2(8 • 6) = 336 + 96 = 432

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