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The question you provided is about calculating the arc length of a circle, given specific parameters. Here’s the breakdown of the problem:

### Given:
- ∠KPL = 135°
- The radius \(PK = 12 \, \text{cm}\)

### Formula for arc length:
The formula for the arc length \(s\) of a circle is:
\[
s = 2\pi r \times \frac{\theta}{360^\circ}
\]
where:
- \(r\) is the radius of the circle
- \(\theta\) is the central angle in degrees

### Step-by-step solution:
1. **Identify the given values**:
   - Radius \(r = 12 \, \text{cm}\)
   - Central angle \(\theta = 135^\circ\)

2. **Apply the arc length formula**:
\[
s = 2\pi \times 12 \times \frac{135}{360}
\]
Simplify the fraction:
\[
\frac{135}{360} = \frac{3}{8}
\]
Now, calculate the arc length:
\[
s = 2\pi \times 12 \times \frac{3}{8} = 24\pi \times \frac{3}{8} = 9\pi \, \text{cm}
\]

### Answer:
The arc length \(KL\) is \(9\pi \, \text{cm}\).

Thus, the correct answer is **option b. 9π cm**.

Would you like more details on the steps or have any additional questions?

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Here are 5 related questions you could explore:
1. How do you calculate the area of a sector given the central angle?
2. How would the arc length change if the central angle were 90°?
3. What is the total circumference of the circle?
4. Can you derive the length of the chord \(KL\) instead of the arc length?
5. How is the arc length formula related to the formula for the perimeter of a circle?

### Tip:
Remember, when dealing with circle problems, always check whether the angle is in degrees or radians to apply the correct formulas for arc length and area.

Perhatikan lingkaran P berikut. Diketahui besar ∠KPL = 135°. Jika panjang PK = 12 cm, panjang busur KL adalah . . .

Calculate the arc length of a circle with a central angle of 135° and a radius of 12 cm. This problem applies the arc length formula and is suitable for students in Grades 9-10.

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