https://file.aiquickdraw.com/mathbot/file/1730301435996pa10dj6t.jpg

To find the perimeter (keliling) of the shaded region in the given circle, let's go through the problem step-by-step:

### Given Data
- The radius \( r \) of the circle is 14 cm.
- The central angle \( \angle COD \) is 45°.

### Steps to Solution
1. **Calculate the Arc Length of CD**:
   - Arc length of a sector can be calculated by the formula:
     \[
     \text{Arc Length} = 2 \pi r \times \frac{\theta}{360^\circ}
     \]
     where \( r = 14 \) cm and \( \theta = 45^\circ \).
   - Substitute the values:
     \[
     \text{Arc Length} = 2 \pi \times 14 \times \frac{45}{360}
     \]
   - Simplify:
     \[
     \text{Arc Length} = 2 \pi \times 14 \times \frac{1}{8} = \frac{28 \pi}{8} = 3.5 \pi
     \]
   - Approximating \( \pi \approx 3.14 \):
     \[
     \text{Arc Length} \approx 3.5 \times 3.14 = 10.99 \text{ cm}
     \]

2. **Calculate the Perimeter of the Shaded Region**:
   - The perimeter of the shaded region consists of the arc \( CD \) and the two radii \( OC \) and \( OD \).
   - Adding these lengths:
     \[
     \text{Perimeter} = \text{Arc Length} + OC + OD
     \]
     \[
     \text{Perimeter} \approx 10.99 + 14 + 14 = 38.99 \text{ cm}
     \]

It seems the options provided are different, suggesting a possible misinterpretation or a calculation oversight. Upon review, if there's any scaling error or additional clarification required, it should be clarified.

Let me know if you need further details or a verification for each step! 

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### Further Exploration
1. What is the general formula for the area of a sector?
2. How would the arc length change if the angle were doubled?
3. Can you solve for the perimeter if only a quarter circle is shaded?
4. What if the circle had a radius of 7 cm; how would it affect this problem?
5. Why is understanding arc length essential in real-world applications?

**Tip:** Always double-check calculations involving pi (π) for accuracy when using approximations!

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Find the perimeter of the shaded region in a circle with radius 14 cm and a 45° central angle. This problem involves calculating arc length and perimeter using circle geometry formulas.

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