Finding Total Area of Several RectanglesDate: 07/08/2005 at 21:59:22 From: Chris Subject: Square footage I am trying to calculate the square footage of all the lawn properties I manage, and I am using general rectangles. I multiplied the lengths and widths of each rectangle individually on a spreadsheet and then summed all the square footages to get one number, but when I add up all the lengths and all the widths of the properties and multiply them together I get an entirely different number. Which number is correct? 75 X 100 = 7500 50 X 200 = 10000 90 X 175 = 15750 total 33250 75+50+90 = 215 100+200+175 = 475 215*475 = 102125 Date: 07/08/2005 at 23:00:46 From: Doctor Peterson Subject: Re: Square footage Hi, Chris. Adding the rectangles' areas is the correct way; adding their lengths and widths gives the wrong number. Let's take a simple example to see why. Suppose you have two lawns, one 4 by 6 and one 5 by 5. I'll draw them this way: +---+---+---+---+---+---+ | | | | | | | +---+---+---+---+---+---+ | | | | | | | +---+---+---+---+---+---+ = 24 | | | | | | | +---+---+---+---+---+---+ | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+ | | | | | | +---+---+---+---+---+ | | | | | | +---+---+---+---+---+ | | | | | | = 25 +---+---+---+---+---+ | | | | | | +---+---+---+---+---+ | | | | | | +---+---+---+---+---+ The total area is 24 + 25 = 49. But if you add the lengths and the width, you get an 11 by 9 rectangle, whose area is 99: +---+---+---+---+---+---+-------------------+ | | | | | | | | +---+---+---+---+---+---+ | | | | | | | | | +---+---+---+---+---+---+ | | | | | | | | | +---+---+---+---+---+---+ | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+ | | | | | | | = 99 | +---+---+---+---+---+ | | | | | | | | +---+---+---+---+---+ | | | | | | | | +---+---+---+---+---+ | | | | | | | | +---+---+---+---+---+ | | | | | | | +-----------------------+---+---+---+---+---+ That's a lot of extra area you added on by adding the dimensions! With more than two rectangles, it gets worse. The point of this experiment is, you can't add areas by adding their individual dimensions. You were right the first time. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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