Expert: Paul Klarreich - 6/15/2006

Question
My name is Andy and I have a Parallela pipe.
A (3,1,0)
B (5,1,0)
C (4,5,0)
D (3,1,4)

I need to find the area of it. How should I start it off?

Answer
Hi, Charlie,

One of the major problems I face is that everyone assumes I am familiar with the specialized vocabulary used by their own teachers.  I am not familiar with the term Parallela Pipe.  (Actually I thought that was the name of an actress from the 40's and 50's who specialized in movies of ill repute.)

So please define all your terms exactly, assuming I know nothing of your teacher's or textbook's vocabulary.  Copy out the definitions and the problems exactly, word for word.

However, I can make this suggestion, since you seem to be doing something in 3 dimensions, suggesting vector algebra.

There is an operation called the Vector Product (a.k.a. the 'cross product' of two vectors.  It has the property that given two vectors  <AB> and <AC>, if you find the cross product and take its absolute value, you get the area of the parallelogram spanned by the two vectors, like this:

    C ------------->
   /              /
  /              /
 /              /
/              /
/------------->/
A             B

This concept might help you in finding areas.