Base or Width?Date: 06/11/2002 at 10:12:47 From: Alexis Harrison Subject: Measuring What is the difference between length*width and base*height? They look the same to me, except the figure being measured is rotated. Why do you use two different formulas to measure a parallelogram and square? Thanks, I'm really confused. Date: 06/11/2002 at 12:38:10 From: Doctor Peterson Subject: Re: Measuring Hi, Alexis. These are largely just different terms for the same things, but named differently to remind you of some important details. For a rectangle, we usually refer to the length and width; properly, these are the longer side and the shorter side, respectively, but that really makes no difference. If you set the rectangle horizontally, there is no reason not to call them the "width" and "height": +---------+ | | | |h | | +---------+ w The area is the product of these. For a parallelogram, the important thing to remember is that the "height" is no longer a side of the shape, but the "base" is: +---------+ --- / / | / / h / / | +---------+ ------- b The height is the distance between the top and bottom, measured perpendicular to them. The base is the length of the bottom. If we had said "width", you might think it meant the greatest side-to-side distance, which is not the base: |<-----w?---->| | | | +---------+ --- | / / | | / / h / / | +---------+ ------- b But for a rectangle (which, after all, is a kind of parallelogram!), there is no confusion over the meaning of "width", so you can say that the area is the base times the height or the width times the height. That's why we use the words we do. Does that help? If you think about it, you will realize that you can learn ONLY the formula for the parallelogram, and you can find the area of rectangles and squares as well -- three for the price of one. Realizing that is a big help! - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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