To solve the problem:

Step 1: Formula for the volume of a pyramid

The formula for the volume of a pyramid is:

$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$

Step 2: Find the base area

The base of the pyramid is a rectangle with dimensions 12 cm × 8 cm. The base area is:

$\text{Base Area} = 12 \times 8 = 96 \, \text{cm}^2$

Step 3: Substitute the given volume

The volume of the pyramid is 544 cm³. Substitute into the formula:

$544 = \frac{1}{3} \times 96 \times h$

Step 4: Solve for height $h$

Rearrange the formula to solve for $h$:

$h = \frac{544 \times 3}{96}$

Simplify:

$h = \frac{1632}{96} = 17 \, \text{cm}$

Final Answer:

The perpendicular height of the pyramid is:

$\boxed{17 \, \text{cm}}$

Would you like additional clarification or more details on the calculation steps?

Here are 5 related questions to consider:

1. How do you calculate the volume of a triangular-based pyramid?
2. What happens to the volume if the height doubles?
3. How can you find the height if the base is irregularly shaped?
4. Why is the $\frac{1}{3}$ factor used in the pyramid volume formula?
5. How would this problem change if the base was a triangle instead of a rectangle?

Tip: Always double-check your unit conversions to ensure accuracy when solving geometric problems!