Parallelogram ABCD: Finding the Total Perimeter with Known Side Lengths

To find the perimeter of parallelogram ABCD, we begin by identifying the lengths of its sides:

• Side AB is given as $10$ cm.
• Side BC is given as $8$ cm.

In a parallelogram, opposite sides are equal in length. Therefore, we also know:

• Side CD is $10$ cm (since it is opposite to AB).
• Side DA is $8$ cm (since it is opposite to BC).

The formula for the perimeter $P$ of a parallelogram is:

$P = 2 \times (\text{length}_1 + \text{length}_2)$

Substituting the known values into the formula, we have:

$P = 2 \times (10 + 8)$

$P = 2 \times 18$

$P = 36 \, \text{cm}$

Thus, the perimeter of parallelogram ABCD is $36$ cm.

The correct answer is $\textbf{36 cm}$, which corresponds to choice 3.