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### Miles Squared vs. Square Miles

```
Date: 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/
```
Associated Topics:
Elementary Definitions
Elementary Terms & Units of Measurement
Middle School Definitions
Middle School Terms/Units of Measurement

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