To find the area of the circle using the given circumference of \(8\pi\), Olivia can use the relationships between circumference and area.
The formula for the circumference \(C\) of a circle is:
\[ C = 2\pi r \]
The area \(A\) of a circle is:
\[ A = \pi r^2 \]
To find the area in terms of the circumference, we can derive a formula. From the circumference formula, we can express the radius \(r\):
\[ r = \frac{C}{2\pi} \]
Now we can substitute this expression for \(r\) into the area formula:
\[ A = \pi \left(\frac{C}{2\pi}\right)^2 \]
Simplifying this gives:
\[ A = \pi \cdot \frac{C^2}{(2\pi)^2} = \pi \cdot \frac{C^2}{4\pi^2} = \frac{C^2}{4\pi} \]
Now, since the circumference given is \(C = 8\pi\), we substitute this into the area formula:
\[ A = \frac{(8\pi)^2}{4\pi} = \frac{64\pi^2}{4\pi} = 16\pi \]
However, since we're looking for a method that doesn't require finding the radius first, we note that directly from our derived formula \(A = \frac{C^2}{4\pi}\) can give us the area if we know the circumference.
Thus, Olivia can use the relationship derived to calculate the area, which gives us the option that corresponds with squaring the given circumference and then dividing by \(4\pi\).
So the correct response is:
Olivia should square the given circumference and then divide by \(4\pi\) to find the area of the circle.