To find the area of a circle when given the diameter, we can use the formula for the area of a circle, which is [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle.
Here is the step-by-step process:
1. Find the Radius:
The diameter of Fiona's circle is 14 meters. The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{diameter}{2} = \frac{14 \, \text{meters}}{2} = 7 \, \text{meters}
\][/tex]
2. Calculate the Area:
Using the formula for the area of a circle [tex]\( A = \pi r^2 \)[/tex], we substitute [tex]\( r \)[/tex] with 7 meters.
[tex]\[
A = \pi \times (7 \, \text{meters})^2
\][/tex]
[tex]\[
A = \pi \times 49 \, \text{square meters}
\][/tex]
[tex]\[
A = 49 \pi \, \text{square meters}
\][/tex]
Therefore, after following these steps, we find that the area of Fiona's circle is [tex]\( 49 \pi \)[/tex] square meters.
The correct answer is:
[tex]\[
\boxed{49 \pi \, m^2}
\][/tex]
