Answer
Sample variance = $s^{2}=152.25\text{ sq. feet}$
Sample standard deviation = $s =12.34\text{ feet}$
Work Step by Step
Recall the shortcut formula for calculating the variance ($s^{2}$)$:$
$$s^{2}=\frac{\sum x_{i}^{2}-\frac{(\sum x_{i})^{2}}{n}}{n-1}$$
Create a table in which we compute $\displaystyle \sum x_{i}$ and $\displaystyle \sum x_{i}^{2}.$
$$ \begin{array}{rrr}
& x & x^{2}\\
\hline & 8 & 64\\
& 10 & 100\\
& 32 & 1024\\
& 5 & 25\\
\hline\rm Sum & 55 & 1213
\end{array}$$
Plug in the given values (there are $n=4$ data items).
$$\begin{align*}
s^{2}&= \displaystyle \frac{1213-\frac{(55)^{2}}{4}}{41} & & \\
& =152.25\text{ sq. feet} \\\\
s&= \sqrt{11.4} =12.34\text{ feet}
\end{align*}$$
