Hi Dave,

There are different types of wireless fences but I think the one you are considering has a central transmitter that gives your pet a circular safe region that has an area of one half an acre. One acre is 43560 square feet and the area of a circle is $\pi \; r^2$ square feet where $r$ is the radius in feet and $\pi$ is approximately 3.1416. Thus you have

\[\pi \; r^2 = \frac{43560}{2} = 21780\]

or

\[r = \sqrt{ \left( \frac{21780}{\pi} \right)} = 83 \mbox{ feet.}\]

I hope this helps,
Penny