A sector is 5/12 of a circle of radius 12 cm…

Step 1. The angle. $\dfrac{5}{12} \times 360^\circ = 150^\circ$.

Step 2. The arc. $\dfrac{5}{12} \times 2\pi \times 12 = 10\pi\ \text{cm}$, which is $31.4\ \text{cm}$.

Step 3. The area. $\dfrac{5}{12} \times \pi \times 12^2 = 60\pi\ \text{cm}^2$, which is $188.5\ \text{cm}^2$.