Parallelogram Area with 4:1 Height Ratio: Express in Terms of 2X

To find the area of the parallelogram, we first use the given ratio of 4:1 between the height and side $AB$. This tells us that if side $AB$ is $2X$, then the height must be four times smaller, because we are considering the ratio in terms of the order given $\frac{\text{height}}{\text{AB}} = 4:1$.

Given side $AB = 2X$, the height of the parallelogram is:

$\text{height} = \frac{1}{4} \times 2X = \frac{1}{2}X$.

Now, we calculate the area of the parallelogram using the formula:

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

Here, base = $2X$, and height = $\frac{1}{2}X$.

Thus,

$\text{Area} = 2X \times \frac{1}{2}X = X \times X = X^2$.

Therefore, the area of the parallelogram is $x^2$.