https://file.aiquickdraw.com/mathbot/file/1730162769053rljzs66z.jpg

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.

Find the perimeter of the figure. Use 3.14 for π. (The figure is not to scale, round to at least 1 decimal place).

Learn how to calculate the perimeter of a composite shape with a rectangle and a half-circle. This solution covers step-by-step calculations, including formulas for half-circle circumference and straight-line segments. Suitable for Grades 6-8 students.

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