Areas of Figures Broken into RectanglesDate: 10/17/2001 at 20:16:19 From: Rachel Subject: Area of figures On my sheet it tell me to "Calculate the area of each figure. First divide the figure into rectangles and squares." I have divided them into the rectangles and squares, but I don't know how to find the area. Please help! Thanks, Rachel Date: 10/18/2001 at 11:03:57 From: Doctor Ian Subject: Re: Area of figures Hi Rachel, Once you've divided something into rectangles, +------+-------------+ | A | | | | | +------+ B | | | | +-------------------+ | | C | +-------------+-------------------+ you can find the total area by adding up the areas of the individual rectangles. If you don't see why this is true, you might be a little confused about the meaning of 'area'. If that's the case, you might want to look at this answer from the Dr. Math archives: Area and Perimeter http://mathforum.org/dr.math/problems/jessica.5.1.01.html Think of it this way. Suppose I need to paint the shape I've drawn above. To find out the total amount of paint I need, I would add up the amounts needed to paint the individual rectangles. Does that make sense? So, how do you find the area of a single rectangle? You find two adjacent sides (that is, two sides that touch at a corner) and multiply their lengths: 3 +--------+ | | 2 area = 3 * 2 = 6 | | +--------+ Note that a square is just a special kind of rectangle, in which each pair of adjacent sides has the same length. So the formula still works. You may be able to divide the same shape into rectangles in more than one way, for example: +--------------------+ | | | | +------+ | | | | +-------------------+ | | +---------------------------------+ +------+-------------+ | A | | | | | +------+ B | | | | +-------------------+ | | C | +-------------+-------------------+ +------+-------------+ | A | | | +------+-------------+ | | | +-------------------+ | B | C | +-------------+-------------------+ +--------------------+ | A | | | +------+-------------+ | B | +-------------+-------------------+ | C | +-------------+-------------------+ +------------+-------+ | A | B | | | | +------+-------------+ | C | +---------+---+---------+---------+ | D | E | F | G | +---------+---+---------+---------+ In each case, so long as the individual rectangles cover the whole shape, you'll get the same total area, no matter which rectangles you choose. (Again, if you think of area in terms of paint, it should be clear why this has to be the case.) Generally, you want to choose rectangles where you'll be told (or be able to figure out) the lengths. Often the difference between an easy solution and a hard solution is the way you decide to break a large shape into smaller shapes. It's really not that different from breaking up any large quantity into smaller quantities that are easy to find. For example, suppose you need to know the distance from Long Beach, CA to Chesterton, IN. You might not be able to find a table of distances that will give you that distance directly; but perhaps you can find three other tables that give you the distance from Long Beach to Los Angeles, the distance from Los Angeles to Chicago, and the distance from Chicago to Chesterton. Then you can add those three distances to get the total distance (assuming that you plan to drive through Los Angeles and Chicago on the way). Does this help? Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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