Rectangles and Areas

Date: 09/30/98 at 11:12:51
From: Anonymous
Subject: Re: Math

How do you do area of a shape like a square or rectangle?

Date: 10/04/98 at 02:45:05
From: Doctor Mike
Subject: Re: Math
   
Hello,     

Here is a picture of a typical rectangle:
    
       ***********************************
       *                                 *
       *                                 *
     H *                                 *
       *                                 *
       *                                 *
       ***********************************
                        L   
   
The letter H stands for how high it is and the letter L stands for how 
long it is. If H and L are the same, then the rectangle shape would be 
a square. 

To find out what the area is you just multiply the two numbers 
together, like H times L. For an example, if it is 3 inches high and 
7 inches long, the area is 21 square inches. If it is 7 feet high and 
also 7 feet long (a square), then the area is 49 square feet.  

I hope this helps.

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

Date: 10/04/98 at 11:18:17
From: Anonymous
Subject: Re: Math

Dr. Math, 

What if there are more numbers than just two? For example, what if 
there are 7 numbers all around? Do you multiply all the numbers?

Date: 10/04/98 at 12:48:45
From: Doctor Mike
Subject: Re: Math

Hello again,   

No, you do not get the area by multiplying all the numbers. It's a 
little more involved than that, but not much. What you have to do is 
mentally divide up the shape into pieces that are all rectangles. 
Then use the "Height times Length" rule for each one of those 
rectangles. Finally, add up the areas for all those rectangles to get 
the area of the whole figure. Here's an example:  
      
                             7 
        ******************************************
        *                                        *
        *                                        *
        *                2                       *
        *           ************                 * 4
        *           *          *                 *
        *           *          *2                *
        *           *          *                 *
      6 *           *          *******************
        *           * 4                 3    
        *           *  
        *           *
        *           *
        *     2     *
        *************  
   
You can divide it up into 3 rectangles if you draw 2 vertical lines 
through the figure by extending the 2 vertical lines in the middle (the 
first one from the left with length 4 and the next one with length 2). 
Then the Left part measures 6-by-2, the Middle part measures 2-by-2, 
and the Right part measures 4-by-3. 

                             7 
        ******************************************
        *           |          |                 *
        *          2|          |2                *
        *           |    2     |                 *
        *           ************                 * 4
        *           *          *                 *
        *           *          *2                *
        *           *          *                 *
      6 *           *          *******************
        *           * 4                 3    
        *           *  
        *           *
        *           *
        *     2     *
        *************  

Then the area is:
     
    6*2 + 2*2 + 4*3  =  12 + 4 + 12  =  28 square inches   
   
You could also divide it up into 3 rectangles by drawing just one
horizontal line by extending the 2-inch long horizontal line in the
middle figure. This will yield one long 7-by-2 rectangle at the Top,
and 2 rectangles sticking down. The Left rectangle sticking down
measures 4-by-2 and the Right one measures 2-by-3. 

                             7 
        ******************************************
        *                                        *
        *                                        *
        *     2          2              3        *
        * - - - - - ************ - - - - - - - - * 4
        *           *          *                 *
        *           *          *2                *
        *           *          *                 *
      6 *           *          *******************
        *           * 4                 3    
        *           *  
        *           *
        *           *
        *     2     *
        *************  

So you get:
    
    7*2 + 4*2 + 2*3  =  14 + 8 + 6  =  28 sq. inches   
    
However you divide it up, you will get the same total area answer.   
   
I hope this helps you to understand this process better.     

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