To solve the problem, we need to find the area of the shaded region, which is the area of the larger rectangle minus the area of the inner square.

Here are the steps:

1. Area of the larger rectangle:

   • The dimensions of the rectangle are 12 miles by 15 miles.
   • The area of the rectangle is: $\text{Area of rectangle} = \text{Length} \times \text{Width} = 12 \, \text{mi} \times 15 \, \text{mi} = 180 \, \text{square miles}$

2. Area of the inner square:

   • The dimensions of the square are 7 miles by 7 miles.
   • The area of the square is: $\text{Area of square} = 7 \, \text{mi} \times 7 \, \text{mi} = 49 \, \text{square miles}$

3. Area of the shaded region:

   • The shaded area is the area of the larger rectangle minus the area of the inner square: $\text{Shaded area} = \text{Area of rectangle} - \text{Area of square} = 180 \, \text{square miles} - 49 \, \text{square miles} = 131 \, \text{square miles}$

Thus, the area of the shaded region is 131 square miles.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the perimeter of the larger rectangle?
2. How would the shaded area change if the square's side length increased by 2 miles?
3. How can we compute the area if the dimensions are given in kilometers instead of miles?
4. What if the inner shape was a circle instead of a square—how would you calculate the shaded area?
5. How can you apply this concept to find the area between two different polygons?

Tip: When finding the area of complex shapes, break them down into simple geometric figures and subtract/add their areas as needed.