To find the perimeter of this figure, we’ll add up the lengths of all the outer sides. The shape includes a rectangle attached to a half-circle on one end. Here’s a step-by-step breakdown:

1. Lengths of the Straight Sides:

   • The left vertical side is 8 miles.
   • The bottom horizontal side is 6 miles.
   • The top horizontal side is the length across the rectangle before the half-circle, which is 9 miles.

2. Half-Circle Perimeter:

   • Since the figure has a half-circle, we need to find the circumference of a full circle first, then take half of it.
   • The radius of the half-circle is half of the vertical side (8 miles / 2 = 4 miles).
   • The circumference of a full circle is $2 \pi r$, so for a radius of 4 miles: $2 \times 3.14 \times 4 = 25.12 \text{ miles}$
   • Since it's a half-circle, divide by 2: $\frac{25.12}{2} = 12.56 \text{ miles}$

3. Total Perimeter:

   • Now, add up all these segments: $8 + 6 + 9 + 12.56 = 35.56 \text{ miles}$

The perimeter of the figure is 35.6 miles (rounded to one decimal place).

Would you like more details or have any questions?

Related Questions

1. How do we calculate the perimeter of a quarter circle?
2. What is the formula for the circumference of a full circle?
3. How would the perimeter change if the radius of the half-circle doubled?
4. How does changing the value of π affect the calculated perimeter?
5. What is the area of this shape?

Tip: Always double-check dimensions and calculations for each part of a composite figure when finding perimeter or area.