To find the perimeter of this composite figure, we need to account for the straight segments and the half-circle on the right side.

Step 1: Identify the Perimeter Components

The perimeter consists of:

1. The left vertical side: $5$ miles
2. The top horizontal side: $6$ miles
3. The bottom horizontal side: $2$ miles
4. The half-circle on the right side.

Step 2: Calculate the Half-Circle's Arc Length

The diameter of the half-circle is equal to the vertical distance on the right side, which is $5$ miles. The radius $r$ is therefore: $r = \frac{5}{2} = 2.5 \text{ miles}$

Since it is a half-circle, the arc length $L$ of the half-circle is: $L = \pi \times r = 3.14 \times 2.5 = 7.85 \text{ miles}$

Step 3: Add All Perimeter Components

Now, we sum up all the straight sides and the half-circle's arc length: $\text{Perimeter} = 5 + 6 + 2 + 7.85 = 20.85 \text{ miles}$

Final Answer:

The perimeter of the figure is approximately: $\boxed{20.9 \text{ miles}}$

Let me know if you'd like any further details or have questions!

Here are five questions that expand on this topic:

1. What would the perimeter be if the figure had a full circle instead of a half-circle?
2. How would the perimeter change if the bottom length increased from 2 miles to 4 miles?
3. How do you find the area of a composite figure like this one?
4. What formula would you use if the half-circle had a different diameter?
5. How would the perimeter calculation change if the half-circle were on the left side instead?

Tip: When working with composite shapes, separate each component to simplify perimeter or area calculations.