# 12.2 Surface Area of Prisms & Cylinders

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12.2 Surface Area of Prisms & Cylinders

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)

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

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. 60o 10 in.

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

Let’s look at lateral area 1st! So, SA = 2B + Circumference × h
Thm 12.3: SA of a rt. cylinder Let’s look at lateral area 1st! LA = Circumference × h or LA = 2rh So, SA = 2B + Circumference × h SA = 2r2 + 2rh

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