12.2 Surface Area of Prisms & Cylinders

DefinitionsDefinitions• Prism – polyhedron with 2 faces (called

bases) that lie in planes.– Named by the shape of the bases.

• Lateral Faces – the faces that are NOT bases (all are ’ogram shaped)

• Lateral Edges – edges of the lateral faces that are NOT edges of the bases as well.

• Height (altitude) - distance between the bases.

• Right Prism – lateral edges are to bases.• Oblique Prism – lateral edges are NOT

to the bases. (looks slanted)

Right Oblique

Triangular PrismsTriangular Prisms

Bases (2 Δs)

Lateral edges (3)

Lateral faces (3 ll’ograms)

height

3-D Areas

• Lateral Area (LA) – the sum of the areas of the lateral faces only.– Does not include the area of the bases.

• Surface Area (S) – the sum of the areas of ALL the faces.– Lateral area + area of the bases

Net• Defn. – a 2-dimensional

representation of a solid.

• Just think “unfold” the figure and lie it flat.

• Ex:

To find surface or lateral areas, you could find the areas of each individual

face and then add them all together; OR you could use formulas!

Thm 12.2 – SA of a rt. Prism

SA = 2B + Ph

B = area of base, P = perimeter of base, h = height of prism

What about Lateral Area?

* remember: LA is everything BUT the bases!

So, LA = Ph

Ex: Find the lateral & surface areas of the triangular prism.

6 in

.

10 i

n.

4

32sB

4

336 39

60o

Cylinder• Defn. – solid with , circular bases.

• Can be right or oblique.

• Lateral Area – the area of the curved surface.

What does the curved surface look like if lied out flat?

Think of the label of a soup can!

It’s a rectangle! (area of rectangle = bh)

• Surface Area – lateral area + area of bases.

h

h

Thm 12.3: SA of a rt. cylinderLet’s look at lateral area 1st!

LA = Circumference × h

or

LA = 2rh

So, SA = 2B + Circumference × h

or

SA = 2r2 + 2rh

Ex: Find the lateral & surface areas of the cylinder.

LA = 2rh

LA = 2(4)(8)

LA = 64 m2

SA = 2r2 + 2rh

SA = 2(42) + 64SA = 32 + 64

SA = 96 m2

8 m

.

4 m.