1. 12.2 Surface Area of
Prisms & Cylinders
p. 728
NCSCOS: 1.02, 2.03, 2.04

2. 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)

3. Right Oblique
Triangular PrismsTriangular Prisms
Bases (2 Δs)
Lateral edges (3)
Lateral faces (3 ll’ograms)
height

4. 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

5. Net
• Defn. – a 2-dimensional
representation of a solid.
• Just think “unfold” the figure and lie it
flat.
• Ex:

6. 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
S = 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

7. Ex: Find the lateral & surface
areas of the triangular prism.
LA = Ph
P = 6*3 = 18
LA = 18*10
LA = 180 in2
S = 2B + Ph
S = 2(15.59) + 180
S = 31.18 + 180
S = 211.18 in2
6
in.
10in.
B=
s
2
√3
4
=
36√3
4
=9√3 ¿15.59
60o

8. 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

9. Thm 12.3: SA of a rt. cylinder
Let’s look at lateral area 1st
!
LA = Ch
or
LA = 2πrh
So, S = 2B + Ch
or
S = 2πr2
+ 2πrh

10. Ex: Find the lateral & surface
areas of the cylinder.
LA = 2πrh
LA = 2π(4)(8)
LA = 64π m2
Or 201.06 m2
S = 2πr2
+ 2πrh
S = 2π(42
) + 64π
S = 32π + 64π
S = 96π m2
Or 301.59 m2
8m.
4 m.

11. You can find SA of cylinder
records used on photographs
during 1800s.
http://history.sandiego.edu/GEN/recording/notes.html