Area: Triangle vs. Rectangle

Date: 4/30/96 at 12:2:36
From: Anonymous
Subject: Math

Dear Dr.Math,

Why do you have to use a different formula to get the area of a 
triangle than a rectangle or square?

Date: 5/4/96 at 16:54:44
From: Doctor Mike
Subject: Re: Math

Greetings,
  
You use a different formula because it is a different problem.
The answer is different so you need a different process to get
the answer.  

There is another way to explain this with a picture. Here is a
rectangle with a line drawn from one corner to the opposite corner:
  
          ------------
          |\         |
          | \        |
          |  \       |
          |   \      |
          |    \     |
          |     \    |
          |      \   |
          |       \  |
          |        \ |
          |         \|
          ------------
  
The rectangle is about 2 cm wide and 4 cm tall, so its area is 
2 times 4 , which is 8 square cm.  Clearly, the rectangle is made up
of the 2 triangles.  If you used the same formula to get the area
of the triangles you would get the wrong answer.  Each triangle is
one half the area of the whole rectangle.  You get that if you use
the correct formula for the area of the trangle, which is "Base 
times Altitude times 1/2".  
  
I hope that was clear.  If you have any more questions please write
us again.  

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/