The base of a parallelogram is twice its height. If the area of the parallelogram is $338{\text{cm}}^2$, then find its height (in $\text{cm}$).

Let the height of the parallelogram be $h\text{cm}$.
According to the question, the base ($b$) is twice its height:

$$b=2h$$

The area of a parallelogram is given by the formula:

$$\text{Area}=\text{base}\times \text{height}$$

$$338=2h\times h$$

$$338=2h^2$$

$$h^2=\frac{338}{2}$$

$$h^2=169$$

$$h=\sqrt{169}=13\text{cm}$$

Therefore, the height of the parallelogram is $13\text{cm}$.