To find the area of a regular octagon inscribed in a circle of radius \( r \), we can use the formula:
\[ A = 2 \times (1 + \sqrt{2}) \times r^2 \]
Given that the radius of the circle is 4 meters, \( r = 4 \).
Substitute the value of \( r \) into the formula:
\[ A = 2 \times (1 + \sqrt{2}) \times (4)^2 \]
\[ A = 2 \times (1 + \sqrt{2}) \times 16 \]
\[ A = 32 \times (1 + \sqrt{2}) \]
\[ A \approx 32 \times (1 + 1.414) \]
\[ A \approx 32 \times 2.414 \]
\[ A \approx 77.408 \, \text{square meters} \]
So, the area of the regular octagon inscribed in a circle of radius 4 meters is approximately \( 77.408 \, \text{square meters} \).
