To find the area of a circle, you can use the formula:
\[ \text{Area} = \pi r^2 \]
where \( r \) is the radius of the circle. In this case, the diameter of the circle is given as 82 mm, so the radius \( r \) is half of the diameter:
\[ r = \frac{82 , \text{mm}}{2} = 41 , \text{mm} \]
Now, substituting the radius into the area formula and using \( \pi \approx 3.14 \):
\[ \text{Area} = 3.14 \times (41 , \text{mm})^2 \]
Calculating \( (41 , \text{mm})^2 \):
\[ (41 , \text{mm})^2 = 1681 , \text{mm}^2 \]
Now, calculate the area:
\[ \text{Area} = 3.14 \times 1681 , \text{mm}^2 \approx 5277.34 , \text{mm}^2 \]
Rounding to the nearest hundredth, the area of the circle is:
\[ \text{Area} \approx 5277.34 , \text{mm}^2 \]
Thus, the area of the circle is approximately 5277.34 mm².