To find the internal area of a circular ice rink, we can use the formula for the area of a circle, which is given by:
\[ A = \pi r^2 \]
where \( A \) is the area and \( r \) is the radius of the circle.
First, we need to calculate the radius of the ice rink. The radius is half of the diameter. Given that the diameter is 20.4 meters, we calculate the radius as follows:
\[ r = \frac{\text{diameter}}{2} = \frac{20.4 \text{ m}}{2} = 10.2 \text{ m} \]
Now we can substitute the radius into the area formula:
\[ A = \pi (10.2 \text{ m})^2 \]
Calculating \( 10.2^2 \):
\[ 10.2^2 = 104.04 \text{ m}^2 \]
Now we can plug this value into the area formula:
\[ A = \pi \times 104.04 \text{ m}^2 \]
Using \( \pi \approx 3.14159 \):
\[ A \approx 3.14159 \times 104.04 \text{ m}^2 \approx 326.72 \text{ m}^2 \]
Thus, the internal area of the ice rink is approximately:
\[ \boxed{326.72 \text{ m}^2} \]
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