To find the area of a dime using its circumference, we can start by using the formula for the circumference of a circle:
\[ C = 2\pi r \]
Where \( C \) is the circumference and \( r \) is the radius. Given that the circumference of the dime is 53.38 millimeters, we can rearrange the formula to solve for the radius:
\[ r = \frac{C}{2\pi} \]
Using \( \pi \approx 3.14 \):
\[ r = \frac{53.38}{2 \times 3.14} \approx \frac{53.38}{6.28} \approx 8.5 \text{ millimeters} \]
Now that we have the radius, we can use it to find the area \( A \) of the dime using the formula for the area of a circle:
\[ A = \pi r^2 \]
Substituting the value of \( r \) and using \( \pi \approx 3.14 \):
\[ A \approx 3.14 \times (8.5)^2 \] \[ A \approx 3.14 \times 72.25 \approx 226.385 \]
Rounding this to the nearest tenth, we find:
\[ A \approx 226.4 \text{ square millimeters} \]
Therefore, the area of the dime is approximately 226.4 square millimeters.