Is there a way to find the height...or area of a parallelogram using coordinates?

[PingSpike]

I'm sure there is, but I'm apparently to stupid to figure it out. Every formula I look up for area says to use height to determine it. Which is fine but every formula to determine height says to use the area. That's great. All I have are the coordinates and therefore the length of all sides. I can assume its a parallelogram.

 

[blinblue]

The area = a*b*sin(theta). 'a' being the length of one side 'b' being the other, and theta being the angle between the two. And all of that would be fairly easy to get from the points.

 

[esun]

Off the top of my head you should be able to get the height using a dot product to find the projection of one side onto an adjacent side and using simple trigonometry after that.

It may help to look at the diagram on this page under "Geometric Interpretation":

http://en.wikipedia.org/wiki/Dot_product

You can use the dot product to get the magnitude of one side projected onto the other as well as the angle between them. Then you can use the law of cosines to find the last side of the triangle, giving you the height of the parallelogram.

 

[Aluvus]

Several solutions: http://mathworld.wolfram.com/Parallelogram.html

More, less reliable and using worse notation: http://en.wikipedia.org/wiki/Parallelogram

You have the length of all sides, and also you can determine the angles. Essentially you know or can determine everything about the parallelogram.

 

[PingSpike]

Thanks guys, those links got me unstuck.