Find the area of the following triangles and the height of a triangle given its area and base.

The base $b = 5.4$ cm and the height $h = 5.4$ cm.

The area $A = \frac{1}{2} \times b \times h$.
$$
A = \frac{1}{2} \times 5.4 \text{ cm} \times 5.4 \text{ cm}
$$

$$
A = \frac{1}{2} \times 29.16 \text{ cm}^2
$$
$$
A = 14.58 \text{ cm}^2
$$
The area of the first triangle is $\boxed{\text{14.58 cm}^2}$.

The base $b = 12$ cm and the height $h = 2$ cm.

The area $A = \frac{1}{2} \times b \times h$.
$$
A = \frac{1}{2} \times 12 \text{ cm} \times 2 \text{ cm}
$$

$$
A = \frac{1}{2} \times 24 \text{ cm}^2
$$
$$
A = 12 \text{ cm}^2
$$
The area of the second triangle is $\boxed{\text{12 cm}^2}$.