How to solve this

The length of an arc $L$ is given by the formula:

$$L = \frac{\theta}{360^\circ} \times 2\pi r$$

where $\theta$ is the angle of the sector and $r$ is the radius.

Given $\theta = 150^\circ$ and $r = 12$ cm.

$$L = \frac{150^\circ}{360^\circ} \times 2\pi (12)$$

$$L = \frac{150}{360} \times 24\pi$$ $$L = \frac{5}{12} \times 24\pi$$ $$L = 5 \times 2\pi$$ $$L = 10\pi$$

The length of the arc ABC is $\boxed{\text{10\pi cm}}$.

The area of a sector $A$ is given by the formula:

$$A = \frac{\theta}{360^\circ} \times \pi r^2$$

where $\theta$ is the angle of the sector and $r$ is the radius.

Given $\theta = 150^\circ$ and $r = 12$ cm.

$$A = \frac{150^\circ}{360^\circ} \times \pi (12)^2$$

$$A = \frac{150}{360} \times \pi (144)$$ $$A = \frac{5}{12} \times 144\pi$$ $$A = 5 \times 12\pi$$ $$A = 60\pi$$

The area of the sector OABC is $\boxed{\text{60\pi cm}^2}$.