Geometry 12.1 Prisms

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

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

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

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

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

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 LA = [2(6) +2(4)] 8 = 160 square units 6 4 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 LA = (6 4) = = 208 square units 6 4 8

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

Exercises Find the (a) lateral area and (b) total area of each right prism. 3. (a) LA = pH LA = 1120 cm² (b) TA = LA + 2B TA = (180) TA = 1480 cm² LA = (56)(20) 20 cm 13 cm 10 cm 13 cm A = hm Base is a trapezoid A = 1215 = 180 P = = 56 H = 20 13

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

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

Exercises = 4p p = V = BH 576 = 48H H = l w2046 H1064 L.A. 216 T.A. V = 2(15) + 2w 2w = 24 w = TA = LA + 2B = (1512) = = V = BH = (1512) 4 = LA = pH = [2(8) + 2(6)] 12 = 336 TA = LA + 2B = (86) = = l w h

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