Calculate Parallelogram Area: Finding Expression with Base 13 and Height 4a

To find the area of the given parallelogram, we apply the formula for the area of a parallelogram, which is:

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

Here, the base is given as $13$ cm and the height is given as $4a$.

Plugging these values into the formula, we have:

$\text{Area} = 13 \times 4a$

Simplifying this, we get:

$\text{Area} = 52a$

Therefore, the area of the parallelogram, expressed in terms of $a$, is $\boxed{52a}$ cm².

The correct choice from the given options is therefore choice 3: $52a$ cm².