The area of a triangle is calculated using the formula:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
With a Base of 12 cm and a Height of 5 cm, substituting these values yields:
\[
\text{Area} = \frac{1}{2} \times 12 \times 5 = 30 \, \text{cm}^2
\]
The triangle's area is 30 cm\(^2\). This corresponds to option (1).