Variance in different measurements

Question

What is the best way to convert variance in one measurement unit to variance in another measurement unit? For example:

The variance of the heights of the mango trees in your garden is 13 square feet. What will be the variance in yards?

Answer 1

As a general property of variance, $\text{Var}(cX) = c^2\text{Var}(X)$ where $X$ is a random variable and $c$ is a constant. Converting $X$ from being in feet to yards would be using $c=\frac{1}{3}$, so your variance should be $\frac{13}{9}$ yards squared.