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.