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 ($b$) of the parallelogram is twice its height:

$$b=2h$$

The formula for the area of a parallelogram is:

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

Given that the area is $338{\text{cm}}^2$:

$$2h\times h=338$$

$$2h^2=338$$

$$h^2=\frac{338}{2}=169$$

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