Calculating Square Footage or AreaDate: 01/08/2007 at 07:34:47 From: Melissa Subject: square footage I recently got a job at a home improvement store, and I am constantly asked to figure out square footage. I need the formula that is used on most areas like square and rectangle. Also, what if a wall is not square like a triangle or odd shape. Date: 01/08/2007 at 16:05:27 From: Doctor Peterson Subject: Re: square footage Hi, Melissa. The basic formulas are: Rectangle: A = lw (area = length times width) Triangle: A = bh/2 (area = base times height divided by 2) The triangle formula really means that the area of any triangle is 1/2 that of a rectangle with the same base and height: +----+--------------+ | /...\ | | /.......\ |h | /...........\ | |/...............\ | +-------------------+ b With these two formulas, which are really almost just one formula, you can find the area of any region with straight edges, by breaking it up into rectangles and triangles. For example, suppose you had to find the area of this shape: 12 +-------------------------------+ | | | |3 | | | +-------------+ | | 5 | | 11| |4 | | | + | / | / | / | / | / + You can break it up several ways. Here is one: 12 +-----------------+-------------+ | | | | | A |3 | | | | B +-------------+ | | 5 | | 11| |4 | | +-----------------+ | / | C / | / | / | / + We have to find the length and width of each piece. Since the width of piece A is 5, it uses up 5 feet of the top edge, leaving 12-5 = 7 feet for piece B's width. Similarly, piece A is 3 feet high, so the total height of piece B is 3+4 = 7 feet. That means that piece B is a square 7 by 7 feet. How about piece C? Its width is the same as B (7 feet); and since B's height of 7 feet uses up 7 of the 11 feet of the total height, C's height is 11-7 = 4 feet. That means the base of C is 7 feet, and its height is 4 feet. 7 5 +-----------------+-------------+ | | | | |3 A |3 | | | |7 B +-------------+ | | 5 | | | |4 | 7 | +-----------------+ | / | C / |4 / | / | / + The area, then, is Area = Area A + Area B + Area C = 3*5 + 7*7 + 7*4/2 = 15 + 49 + 14 = 78 square feet If you ever have to measure anything round, you'll need the formulas for a circle, but that's probably not common in your everyday work. Let me know if you'd like them. I'd recommend that you look in your library or bookstore for a review book on basic geometry or practical math that has a chapter on this sort of problem. Doing a few exercises after looking through how they demonstrate it in the book will probably help a lot. It's a lot easier to learn something like this when you have a reason (such as being paid for doing it!) than it probably was in school. 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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