To find the area of the shaded region, we need to interpret the figure, assuming it consists of two circles with different radii based on the measurements provided:

1. Outer Circle:

   • Radius = $7$ inches
   • Area of the outer circle = $\pi \times (7)^2 = 49\pi$ square inches

2. Inner Circle:

   • Radius = $3.5$ inches (converted from "3 and one-half inches")
   • Area of the inner circle = $\pi \times (3.5)^2 = 12.25\pi$ square inches

3. Shaded Region:

   • The shaded area is the area of the outer circle minus the area of the inner circle.
   • Area of the shaded region = $49\pi - 12.25\pi = 36.75\pi$ square inches

Using $\pi \approx 3.14159$, $36.75 \pi \approx 36.75 \times 3.14159 \approx 115.5 \text{ square inches}$

Answer:

The area of the shaded region is approximately 115.5 square inches.

Would you like a detailed explanation of each step or have any questions?

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Here are five related questions you might consider:

1. How would the area change if the inner circle radius were doubled?
2. What is the difference in area if the outer radius were increased by 1 inch?
3. How would the area calculation change if we used different approximations of $\pi$?
4. What is the area of the shaded region if the inner circle were replaced by a square with the same area?
5. How would the problem change if the circles were concentric ellipses instead?

Tip: Always check if units are consistent throughout the problem to avoid calculation errors.