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The problem in the image involves finding the area of a shaded segment in a circle. Let's go through the information presented in the image to solve it.

The image shows a circle with a sector, and the central angle of the sector is labeled as 120°. The radius of the circle is given as 6 cm.

To find the area of the shaded segment, we can use the formula for the area of a sector and the formula for the area of a triangle formed by the radii and the chord.

### Step-by-step Solution:

1. **Find the area of the entire sector:**

   The area of a sector of a circle is given by:

   \[
   \text{Area of the sector} = \frac{\theta}{360} \times \pi r^2
   \]

   where:
   - \(\theta = 120^\circ\) (central angle of the sector)
   - \(r = 6\) cm (radius of the circle)

   Substituting the values:

   \[
   \text{Area of the sector} = \frac{120}{360} \times \pi \times 6^2 = \frac{1}{3} \times \pi \times 36 = 12\pi \, \text{cm}^2
   \]

2. **Find the area of the triangle formed by the radii and the chord:**

   The triangle formed within the sector is an equilateral triangle (since the central angle is 120° and the two radii are equal).

   The area of the triangle can be found using the formula:

   \[
   \text{Area of the triangle} = \frac{1}{2} r^2 \sin(\theta)
   \]

   where:
   - \(r = 6\) cm
   - \(\theta = 120^\circ\)

   Substituting the values:

   \[
   \text{Area of the triangle} = \frac{1}{2} \times 6^2 \times \sin(120^\circ)
   \]

   Knowing that \(\sin(120^\circ) = \frac{\sqrt{3}}{2}\):

   \[
   \text{Area of the triangle} = \frac{1}{2} \times 36 \times \frac{\sqrt{3}}{2} = 9\sqrt{3} \, \text{cm}^2
   \]

3. **Find the area of the shaded segment:**

   The area of the shaded segment is the area of the sector minus the area of the triangle:

   \[
   \text{Area of the shaded segment} = 12\pi - 9\sqrt{3} \, \text{cm}^2
   \]

### Conclusion:
The area of the shaded segment is:

\[
12\pi - 9\sqrt{3} \, \text{cm}^2
\]

This corresponds to option **D** in the given choices.

Would you like more details or have any questions?

### Related Questions:
1. How do you find the area of a segment when the central angle is given in radians?
2. What is the formula for the area of a triangle when all three sides are known?
3. Can you explain how to find the length of an arc of a circle?
4. What happens to the area of a sector if the radius is doubled?
5. How do you calculate the perimeter of a sector in a circle?

### Tip:
Remember that for sectors, both the radius and the central angle are crucial for calculations, so make sure to always check if the angle is given in degrees or radians!

Luas lingkaran pada gambar tersebut adalah ...

Learn how to calculate the area of a shaded segment in a circle with a 120-degree central angle and a 6 cm radius. This problem uses geometry and trigonometry concepts, involving the formulas for the area of a sector and an equilateral triangle. Suitable for students in Grades 9-11.

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