I've seen how to visualize the formula for getting the area of a parallelogram. The first picture shows 2 ways which give the same result of Area = base * height.
http://tinypic.com/view.php?pic=2na1kr7&s=5 (link to first pic)
However, the first time I thought about it before being show the actual formula, I thought it was Area = side * side.
http://tinypic.com/view.php?pic=2rhpbvk&s=5 (link to second pic)
The 2 sides of the parallelogram are 2 vectors, x and y.
If you place copies of vector y length of x times along the vector x, and then you add all lengths of vector y's (which is the same as length of vector y * length of vector x), it seems like you also get the area of the parallelogram.
I know that you'll end up with a different result since the height is always less than the length of the vector y (unless they were parallel) but the method in the second picture seems correct.
I also haven't seen the second picture's method being taught online so I'm guessing it's actually incorrect. What I want to know is what makes it incorrect because it really seems like it's correct despite giving a different answer from the usual base * height formula.
Thanks in advance for any help.