Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 11-4
		
Example 1	Surface Area of Prisms
Find the lateral area and surface area of each prism.
a.  Find the lateral area.              	Find the surface area.
         L	 = Ph		S	= L + 2B		
		= (2 + 2w)(h)		= L + 2w			
		= (2 · 15 + 2 · 4)(6)		= 228 + 2(15)(4)
		= 228 in^2		= 348 in^2
b.  The lateral area is made up of bases that are not parallel.
	   L = Ph	Write the formula.
		= (4.5 + 6 + 7.5)(5)	P is perimeter of the triangular base.  h is the height of the prism.
		= 90 in^2	Simplify.
	Find the surface area.
	  S	= L + 2B	Write the formula.
		= L + 2(bh)	B = bh (area of triangle)
		= 90 + 2(· 4.5 · 6)	Substitution.
		= 117 in^2	Simplify.

Example 2	Surface Area of a Cylinder                                                            
Find the lateral area and surface area of the cylinder.  
Round to the nearest tenth.                                                                            
                                                                                                                   
Estimate (2 · 3 · 6 · 15) + (2 · 3 · 6^2) or 756 cm^2
Lateral Area                                                  Surface Area                                                              
L = 2πrh	                   S 	= L + 2πr^2
	= 2π(6)(15)		= 180π + 2π(6)^2
	= 180π	exact answer		= 252π 	        exact answer
	≈ 565.5 cm^2	approximate answer       	≈ 791.7 cm^2     approximate answer                                                                                                                                  

How does your estimate compare to your answer?
Example 3	Compare Surface Areas
PACKAGING	A manufacturing company is deciding between two packaging styles. The first is a rectangular prism having length 4 inches, width 3 inches and height 5 inches. The second is a cylinder having radius 4 inches and height 6 inches.  Which style has the least surface area?

Surface Area of Rectangular Prism Style
           Lateral Area                      Area of Bases
                                             
     S	=      L                   +                2B                       
	=     Ph                  +               2w   
	= (2 · 4 + 2 · 3)(5) +             2(4)(3)
	= 94 in^2	

Surface Area of Cylinder Style
                 Lateral Area                      Area of Bases

     S	=            L                   +                2B                       
	=         2πrh                +               2πr^2
	=       2π(4)(6)             +             2π(4)^2
	≈ 251.3 in^2

Since 94 in^2 < 251.3 in^2, the rectangular prism style has the least surface area.