To find the area of a circle, you can use the formula:
\[ \text{Area} = \pi r^2 \]
Where \( \pi \) is approximately 3.14, and \( r \) is the radius of the circle.
Given that the diameter of the circle is 82 mm, the radius \( r \) is half of the diameter:
\[ r = \frac{82 \text{ mm}}{2} = 41 \text{ mm} \]
Now, substitute the radius into the area formula:
\[ \text{Area} = 3.14 \times (41 \text{ mm})^2 \]
First, calculate \( (41 \text{ mm})^2 \):
\[ (41 \text{ mm})^2 = 1681 \text{ mm}^2 \]
Now plug this value into the area formula:
\[ \text{Area} = 3.14 \times 1681 \text{ mm}^2 \]
Now perform the multiplication:
\[ \text{Area} = 5267.34 \text{ mm}^2 \]
Finally, round to the nearest hundredth:
\[ \text{Area} \approx 5267.34 \text{ mm}^2 \]
Thus, the area of the circle is about 5267.34 mm².