Generally, carpet covers the entire floor area, so the ceiling height and door area are irrelevant. The floor area is the product of its length and width.
... floor area = (16 ft)×(13 ft) = 208 ft²
_____
If your 3" overhang has to do with carpeting the floor, then the required area would seem to be (16.5 ft)×(13.5 ft) = 222.75 ft².
