The problem involves a circle inscribed in a square, and you're asked to find the area of the shaded region between the square and the circle.

Step 1: Circle's Radius and Area

The given diameter of the circle is 24 meters, so the radius $r$ is: $r = \frac{24}{2} = 12 \, \text{m}$ The area $A_{\text{circle}}$ of the circle is given by the formula: $A_{\text{circle}} = \pi r^2 = \pi (12)^2 = 144\pi \, \text{m}^2$ Approximating $\pi \approx 3.1416$: $A_{\text{circle}} \approx 144 \times 3.1416 = 452.39 \, \text{m}^2$

Step 2: Square's Side Length and Area

Since the circle is inscribed, the diameter of the circle is equal to the side length of the square, so the side length $s$ of the square is: $s = 24 \, \text{m}$ The area $A_{\text{square}}$ of the square is: $A_{\text{square}} = s^2 = 24^2 = 576 \, \text{m}^2$

Step 3: Shaded Area

The shaded area is the difference between the area of the square and the area of the circle: $A_{\text{shaded}} = A_{\text{square}} - A_{\text{circle}} = 576 - 452.39 = 123.61 \, \text{m}^2$ Rounding to the nearest whole number: $A_{\text{shaded}} \approx 124 \, \text{m}^2$

Thus, the area of the shaded region is approximately 124 m².

Would you like any more details or have any questions?

Related Questions:

1. What is the area of a circle with a diameter of 36 meters?
2. How would the shaded area change if the diameter of the circle was increased by 50%?
3. What is the perimeter of the square?
4. How does the area of the square relate to the diameter of the circle?
5. How would the problem change if the circle was circumscribed around the square?

Tip: Always remember that for a circle inscribed in a square, the diameter of the circle equals the side length of the square.