Units and Square Units in Measuring Perimeter and Area
Date: 01/02/2005 at 14:46:37 From: Michelle Subject: Unit vs. Square Units and Perimeter and Area Why is perimeter measured in units whereas area is measured in squared units? I understand that perimeter is one-dimensional whereas area is two- dimensional, but I just don't understand why one is units while the other is squared units.
Date: 01/02/2005 at 17:37:20 From: Doctor Rick Subject: Re: Unit vs. Square Units and Perimeter and Area Hi, Michelle. Let's be a bit clearer: Perimeter is measured in units OF LENGTH, while area is measured in units OF LENGTH squared. For instance, perimeter can be measured in meters, while area can be measured in square meters. Now imagine how you might measure a perimeter and an area physically. To measure the perimeter of a shape, you might take a string, lay it along the outer edge of the shape until you come back to the start of the string, and cut it off there. Straighten out the string and measure its length: that's the perimeter of the shape. Can you do the same with the area? No! You might try to fill the shape with string, but how much string it takes will depend on the thickness of the string--it's not just a matter of how long the string is. Instead, we can imagine cutting a whole bunch of little squares--say, one centimeter on each side--out of paper. Then we can lay the squares side by side inside the shape until we have filled all the space. (We may have to cut up some of the squares into smaller pieces and stick them in little corners.) Count up all the squares we used, and what do you have? The area of the shape in SQUARE CENTIMETERS! In other words, a shape with an area of, say, 25 square centimeters has an area 25 times as great as that of a square one centimeter on a side. That's where the notion of "square units" comes from. Furthermore, the area of a rectangle (including a square) is the product of its length and width. (This is easily confirmed by the method of cutting up little squares: they go in rows, and you can count them by multiplying the number of rows by the number in each row.) So the area of the one-centimeter square is (1 cm) * (1 cm) = 1 cm*cm The units are centimeters times centimeters. What is a number times itself? It's the square of the number. So we call centimeters times centimeters "square centimeters". How's that? Does it answer your questions? Let me know. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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