Surface Area of Prisms and Cylinders

12.2

California State Standards

8, 9: Solve problems involving the surface area lateral area of geometric solids and

COMMIT TO MEMORY THE

NECESSARY FORMULAS.

definitionsPrism Bases: two congruent, parallel polygons Lateral faces: parallelograms formed by connecting corresponding vertices of the bases. Altitude: the perpendicular distance between its bases. A prism is named for its bases

Triangular PrismRectangular Prism

Pentagonal Prism

definition

Regular Prism The bases are regular polygons The parallelogram faces are congruent

definition

Right Prism The lateral faces are perpendicular to the bases

Oblique Prism The lateral faces are not perpendicular to the bases

definitionsCylinder Bases: two congruent-parallel circles Lateral face: a rectangle connecting the bases Altitude: the perpendicular distance between its

bases.

definitionsCylinder Right Cylinder: a segment joining the centers of the

bases is perpendicular to the bases.

right cylinder

definitions

Surface AreaThe sum of the area of a polyhedron’s faces.

how much wrapping paper is needed for a boxLateral area: the area of the lateral faces

how much paint for the walls of a room.

exampleWhat would the polyhedron look like if laid flat?

back

front

bottomleftside

rightside

leftroof

rightroof

The two-dimensional representation of a three-dimensional figure is called a

NET.

exampleWhat would the cylinder look like laid flat?

top

bottom

“label”

Remember: this is

called a NET.

example

Find the surface area.

16 cm4 cm

9 cm

2(16 4) 2(16 9) 2(4 9)SA

128 288 72SA 2488 cmSA

exampleFind the surface area

4 m

8 m

2(16 ) 8 8SA

32 64SA 296 301.4 mSA

example

Find the surface area.

10 in6 in

6 in 6 in

2142( 3 6 ) 3(6 10)SA

18 3 180SA 2211.2 cmSA