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Chapter 12 Notes: Surface Area and Volume of Prisms

Goal: Students will find the surface area and volume of prisms.

Lateral Area and Surface Area of Prisms

• A f{C sO"" is a polyhedron with two congruent faces, called J""'a •...."i'•......e-.L-'S'-- .that he in parallel planes.

• The other faces, called ltt t-e {'"(I\ \the corresponding "e(nceS

faces, are parallelograms formed by connectingof the bases.

• The segments connecting these vertices are _-'l,....,a"'"-=-k-=--:.crtA.=-:..'_---'ed='-"ffC'P""'-s _

• _ -"--Pt...:....r .•..(SL!.m-4--!--'7=---- __ are classified by the shapes of their ---h-""a~~...,.,."'-'SoL- _

)--,,(

II'

Right Prisms:

• The ~-,-:-h+..!...-'- of a prism is the perpendicular distance between its bases, called an__~O~\~~J~c~---

• A prism may be either ci ~nt or ~--'-I~'--'11'1'-cJ'"---""-e"---------• In a ~ prism, each Jette r~' edge is perpendicular to both bases.• A ---D f"j 5rt1 with lateral edges that are not ~rc'1d I c()lo.'/ to the

bases Is an () b) ,f V e prism.

i~'~Vt.r ~ecbl1JJtarPne::,yY1

• Surface Area of a Right Prism:

o The l"l-erC\ \faces.

area of a prism is the Sd m of the areas of the lateral

o The 5cJ (htc c area of a prism is the Sum of the areas of the lateralfaces and the two bases.

Lateral Area: L.A. = --P--'--h-------Surface Area: S = --fL6 .•....'U3

f--ey;tn.ew:r ~ -,KI-ryrtA::::- >

Ex.3: Find the surface area ofthe right pentagonal prism.

1t::-~G1P.7 -;t{Lf,q~o>,2-S)

·Itz:

• Find the volume of the solid.

Ex.S:

ficm

Ex.6:

....~ ,q ......-:to/ ~cm....

Prrt~c -z: ~h (1,1 .rb~)~ ~(?'f)

Ex.8: The volume of a triangular prism is 1860 em". Its base is a right triangle with legs 24 em and 10em long.

a. Draw and label a diagram.b. Find the area of the base of the prism.c. Find the height of the prism.

-b) It~*h~~ 1J (,LtX 'OJ

~ 12--( '0)ff~ rl-Ocm'J..

c) V~ f3h'I ~ ~o z: t20 l-.,(20 lZO

[hi IS. 5 ern ]Ex.9: The volume of the cube is 90 cubic inches. Find the value ofx.

x

. V~ 531Io~W~= ~.5J

Ex.1 0: Find the volume of the right hexagonal prism.

V==- t3 h:::dl ~ r3 (,)

~5126crn3J

ft~~f~~c,J!,11Z,)fr~ ;;J-1(,J3