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Surface Area of a Box

Date: 03/06/2003 at 19:19:03
From: Brie
Subject: The Surface Area of a Box

How do you find the area of the surface area of a box? There are 6 
sides - top, bottom, right, left, front, and back.


Date: 03/07/2003 at 00:42:45
From: Doctor Ian
Subject: Re: The Surface Area of a Box

Hi Brie, 

Here is a box with width W, height H, and depth D:

          W
      +----------+
  D  /          /| 
    +----------+ |
    |          | |
    |          | | H
    |          | |
    |          | |
    |          | |
    |          | +
    |          |/ 
    +----------+

If we cut the box along the edges, we get something like this:

     +---------------+
   D |               |                     
     +---------------+---+---------------+---+
     |      H        | D |       H       | D |
     |               |   |               |   |
     |W              |   |               |   |
     |               |   |               |   |
     |               |   |               |   |
     +---------------+---+---------------+---+
   D |               |
     +---------------+

(You'll remember this better if you try it with a real box!)

If you can find the area of each rectangle, you can add the areas to
get the total surface area of the box.  

Can you take it from here? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Elementary Three-Dimensional Geometry
Middle School Higher-Dimensional Geometry

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