Calculate room floor area from ceiling height and volume.
Volume is floor area times ceiling height, so dividing a known volume by the height recovers the area — the situation that arises constantly when a ventilation or heating specification is given in cubic feet or cubic metres and you need the footprint. The reason it is worth doing carefully is that the same volume describes very different rooms: 2,400 cubic feet is 300 square feet under an eight-foot ceiling but only 200 under twelve, which changes furniture planning, flooring quantities and lighting layout completely while leaving the air-change calculation identical. Assuming a plan proportion lets plausible length and width fall out of the area, which is enough to sanity-check whether the figure you were given describes the room you are standing in.
Floor area and plan dimensions from volume
Floor area = volume / ceiling height; width = square root(floor area / ratio); length = width x ratio; perimeter = 2 x (length + width)
Because ventilation, heating and air-conditioning specifications are given in cubic units. Air change rates, extract fan sizing and heat loss calculations all work from volume, so a spec sheet often tells you the cubic figure and nothing else.
Only as good as the ratio you assume. The area is exact given the volume and height; length and width are illustrative, so change the ratio if you know the room is long and narrow.
Use the mean height rather than the ridge height. For a simple pitch, average the lowest and highest points; for anything more complex, divide the room into sections and total the volumes.