Is there an easy way to estimate the wet surface (that part of the hull under water) area of a boat ?

Question

If I know, for example, that a displacement boat has a length 12meters, beam 4meters, draught 1.2meters, displacement 16 tons.

Answer 1

Not sure. If, you know the Length at the water line (L.W.L.) you may get a good guess. What I would do for a rough estimate. From bow to widest beam say that is 7 meters. Make a triangle with the base the beam width of 4 meters and center line of triangle 7 meters. Then figure the area of that triangle. If, you not sure of the Stern width. Guess it around 2-3 meters (one side of Trapezoid) beam @ 4 meters (Other side of trapezoid) center line is 5 meters and then draw the side lines and figure the area of this.
Add the area of both and that may be as close as you can get.

I say Trapezoid but, it may be something else, I not a geometry major.

Here my estimate from what you give.
12 meters length. we divide the boat at the beam and have 7 and 5 this totals 12 meters of the full length.
Triangle is 7 meters with 4 meter base. 7 x 4 = 28 and / 2 = 14 sq. meters.
Trapezoid is 4 meters (B2) at the beam and we guess 3 meters (B1) at the stern
B1 + B2 = 7 meters ½ of 7 is 3.5 meters.
14 + 3.5 = 17.5 meters of wet area. This just an estimate. ;-)