Total Area of Multiple Objects

Date: 07/18/2002 at 17:24:26
From: Susan Wahl
Subject: square feet

I have 6 windows and want to know the total square feet.  Do I get 
the square footage of each window and then add them together OR do I 
get the measurements of each window (length by width), add all the 
lengths together, add all the widths together and then get the square 
footage?  I get two different answers and don't know which one is 
correct.  Thank you.

Date: 07/19/2002 at 01:27:10
From: Doctor Jeremiah
Subject: Re: square feet

Hi Susan,

You must do each window separately and then add the square
footage together afterwards.  Here is why:

Say we have two windows. One is 3 feet by 4 feet and one is
5 feet by 2 feet:

   +----3----+
   |         |
   |         |
   4    12   |
   |         |
   |         |
   +---------+-------5-------+
             |               |
             2       10      |
             |               |
             +---------------+

See how much space is used up?  12+10=22 square feet.
But if we add the measurements together before calculating
area we get 3+5=8 feet by 4+2=6 feet.  Clearly a window
that is 8 feet by 6 feet is much bigger than the two individual
windows:

   +----3----+-------5-------+
   |         |               |
   |                         |
   4         |               |
   |                         |
   |         |               |
   +-  --  --+--  --  --  -- +
   |                         |
   2         |               |
   |                         |
   +---------+---------------+

So the square footage of the windows would not be equal to
the square footage of this huge thing.

So do each window separately and then add the square
footage together afterwards.

I hope that helps.

- Doctor Jeremiah, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 07/19/2002 at 10:49:23
From: Susan Wahl
Subject: Thank you (square feet)

Thank you so very much for the prompt answer to my math 
question.  What a wonderful website!  So glad I found you.  
Thank you to everyone who donates their time and knowledge.