| The same way it was calculated before the compartment was flooded.
The LCF is the line about which the ship trims when a weight is moved on the vessel. It is found using the first longitudinal moment of area (i.e. the intergral over the area of {x dx dy}) so that the displacement stays the same for small angles of trim.
For the damaged case like you have, you must first sink and trim the ship before you can calculate the new LCF. Are they looking for an exact answer or is this a mythical "rectangular barge"?
Edit; Just to note, the area is the effective waterplane, so the damaged compartment is excluded.
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A vessel is nothing but a bunch of opinions and compromises held together by the faith of the builders and engineers that they did it correctly. Therefor the only thing a Naval Architect has to sell is his opinion.
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