Subsubsection Area Units
Area is usually expressed in units of lengthsquared e.g. square inches, square meters, square kilometers, however specific area units such as the acre or the hectare are also used.
Here are some basic relations between area units in the US Customary and the SI systems of units:
\begin{align*}
\inch{1}^2 \amp= \inch{1} \times \inch{1}\\
\ft{1}^2 \amp= \inch{144}^2\\
\yd{1}^1 \amp = \ft{9}^2\\
\mi{1}^2 \amp= 27,878,400 \ft{9}^2 = \yd{3,097,600}^2\\
1 \mathrm{\ acre} \amp= \ft{43,560}^2 = \yd{4,840}^2\\
\amp\\
\m{1}^2 \amp = \m{1} \times \m{1}\\
\cm{1}^2 \amp = \m{1/10,000}^2\\
\mm{1}^2 \amp = \m{1/1,000,000}^2\\
\km{1}^2 \amp = \m{1,000,000}^2\\
1 \mathrm{\ hectare} \amp = \m{10,000}^2 = \km{0.01}^2
\end{align*}
Example 2.2.13. Area Conversion 1.
How many square feet are there in 1 square meter?
Answer.
\begin{equation*}
A = \m{1}^2 = \ft{10.76}^2
\end{equation*}
Solution.
\begin{align*}
A \amp = \m{1}^2 \times
\left[\frac{\ft{1}}{\m{0.3048}}\right]
\left[\frac{\ft{1}}{\m{0.3048}}\right]\\
A \amp = \m{1}^2 \times
\left[\frac{\ft{1}}{\m{0.3048}}\right]^2\\
\amp= \ft{10.76}^2
\end{align*}
Note that you must perform the meter to feet conversion twice, once for each meter quantity in the original area.
Example 2.2.14. Area Conversion 2.
How many square kilometers are there in 2.5 square miles?
Answer.
\begin{equation*}
A = \mi{2.5}^2 = \km{6.47}^2
\end{equation*}
Solution.
\begin{align*}
A \amp = \mi{2.5}^2 \times
\left[\frac{\ft{5280}}{\mi{1}}\right]^2
\left[\frac{\m{0.3048}}{\ft{1}}\right]^2
\left[\frac{\km{1}^2}{\m{10^6}^2}\right]\\
\amp= \km{6.47}^2
\end{align*}
Note that you must perform the meter to feet conversion twice, once for each meter quantity in the original area..
