1. 12.2 Surface Area of Prisms & Cylinders

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

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 lay 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 =
S = in2
6 in.
60o
10 in.

8. Cylinder Defn. – solid with , circular bases.
Can be oblique or right.
Lateral Area – the area of the curved surface.
What does the curved surface look like if laid 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. Let’s look at lateral area 1st!
Thm 12.3: SA of a rt. cylinder
Let’s look at lateral area 1st!
LA = Ch or
LA = 2rh
So, S = 2B + Ch
S = 2r2 + 2rh

10. Ex: Find the lateral & surface areas of the cylinder.
LA = 2rh
LA = 2(4)(8)
LA = 64 m2
Or m2
S = 2r2 + 2rh
S = 2(42) + 64
S = 32 + 64
S = 96 m2
Or m2
4 m.
8 m.