The problem provided is asking to find the shaded area, which is the difference between the area of a quarter circle and the area of a semicircle. Here’s how to solve it step by step:

1. Quarter Circle: The radius of the quarter circle is the full length of 7 meters.

   The area of a full circle is given by: $A_{\text{circle}} = \pi r^2$ The area of a quarter circle is then: $A_{\text{quarter circle}} = \frac{1}{4} \pi r^2 = \frac{1}{4} \pi (7)^2 = \frac{49}{4} \pi$

2. Semicircle: The diameter of the semicircle is 7 meters, so the radius is half of that: $r_{\text{semicircle}} = \frac{7}{2} = 3.5 \, \text{meters}$ The area of a semicircle is: $A_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (3.5)^2 = \frac{1}{2} \pi (12.25) = 6.125 \pi$

3. Shaded Area: The shaded area is the difference between the area of the quarter circle and the area of the semicircle: $A_{\text{shaded}} = A_{\text{quarter circle}} - A_{\text{semicircle}} = \frac{49}{4} \pi - 6.125 \pi$ Simplifying: $A_{\text{shaded}} = \left( \frac{49}{4} - 6.125 \right) \pi$

Now, let’s calculate this value.The shaded area is approximately 19.2 m².

Would you like more details or have any questions? Here are some related questions for deeper understanding:

1. How do you calculate the area of a sector of a circle with any angle?
2. What is the formula for finding the area of an arc segment?
3. How do you find the perimeter of a sector or segment in a circle?
4. What is the significance of the radius in determining the area of circular shapes?
5. How do you convert between radians and degrees when working with sectors of a circle?

Tip: When dealing with circular areas, always remember that the area scales with the square of the radius, so doubling the radius will quadruple the area!