Posted by Gilligan on Friday, February 22, 2008 at 10:33pm.
I think you need to get the height * width.
I don't understand why you are using three coordinates for the parallelogram corner points instead of two. Is the parallelogram a tilted plane figure in three dimensions, not located on the x,y plane? Are we supposed to determine the location of the fourth corner?
If this parallelogram really is located in three dimensions, then a quick way to get the area is to take the cross product of the vector from P1 to P2 and the vector from P1 to P3. I think that's what they want you to do. The magnitude of the cross product vector is the area.
P1P2 with an arrow over it is the vector representation of the side that goes from P1 to P2. It would be written
2i + 3j + k
P1P3(with arrow), the adjacent side, would be written
-2 +4j + k
The vector whose magnitude is the parallelogram area is
|i j k|
|2 3 1| = -i +0j +2k
|-2 4 1|
(The 3x3 matrix above, surrounded by | | indicates a determinant).
The area is the magnitude of that vector, which is sqrt5 = 2.236
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