Miles Squared vs. Square MilesDate: 07/09/99 at 07:17:45 From: Connor Wlodarczak Subject: A question of area How are these two different? I don't know! 10 square miles 10 miles square I thought they were the same, but my friend says they are not. Thank you very much, Connor Date: 07/09/99 at 08:50:00 From: Doctor Peterson Subject: Re: A question of area Hi, Connor. Good question. I'm not sure whether there's a difference between "ten miles square" and "ten miles squared," but if this is a mile: +---+ then this is a "one mile square," a square one mile on each side whose area is called one square mile: +---+ | | +---+ and this is ten square miles: +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ But "ten miles square" (or "ten miles squared") means we make a square ten miles on a side: +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ If you count, or think a bit, you'll see that 10 miles square is actually 100 square miles, ten times as much as 10 square miles. Words like "square" and "squared" can be tricky, which is why in math we use symbols rather than words, so we can make it clear exactly what we mean. If you've seen how we write "squared numbers" in math, this can be written as 2 2 (10 miles) = 100 (miles ) (10 miles) squared = 100 (square miles) I hope this makes the difference clear to you. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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