Step 1 :The problem is asking for the area of a wallpaper border on top of the baseboard on a flight of stairs, which is in the shape of a parallelogram.
Step 2 :The formula for the area of a parallelogram is given by \(\text{Area} = \text{base} \times \text{height}\).
Step 3 :In this case, the base of the parallelogram is given as 150 cm and the height is given as 12 cm.
Step 4 :Substituting these values into the formula, we get \(\text{Area} = 150 \times 12\).
Step 5 :Solving this, we find that the area of the border is \(\boxed{1800}\) square cm.