To solve problems related to the sector with radius (r = 12\,\text{cm}) and central angle (\theta = 120^\circ), we use the following formulas:

1. Arc Length of the Sector

The arc length (L) is given by:
[L = \frac{\theta}{360^\circ} \times 2\pi r]
Substitute values:
[L = \frac{120^\circ}{360^\circ} \times 2\pi \times 12 = \frac{1}{3} \times 24\pi = 8\pi \approx 25.12\,\text{cm}]

2. Area of the Sector

The area (A) is given by:
[A = \frac{\theta}{360^\circ} \times \pi r^2]
Substitute values:
[A = \frac{120^\circ}{360^\circ} \times \pi \times 12^2 = \frac{1}{3} \times 144\pi = 48\pi \approx 150.72\,\text{cm}^2]

3. Perimeter of the Sector

The perimeter includes the arc length plus two radii:
[P = L + 2r]
Substitute values:
[P = 8\pi + 2 \times 12 = 8\pi + 24 \approx 49.12\,\text{cm}]

Common Answer (if area was asked): (\boxed{48\pi}) cm² (or (\boxed{151}) cm² approx).

If arc length was asked: (\boxed{8\pi}) cm (or (\boxed{25}) cm approx).

If perimeter was asked: (\boxed{8\pi + 24}) cm (or (\boxed{49}) cm approx).

Assuming the most likely question (area), the answer is (\boxed{48\pi}) cm².

(\boxed{48\pi})

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