You could gain an approximation by treating it as occupying a cuboid of length = (total length - the radiiof the approximately hemicylindrical ends) and of width and thickness the averages of the boards' actual dimensions; then adding the two semicircular volumes. The ends' radii may differ. Then add the volume of the fin, which should be a lot easier to calculate.
To obtain an accurate measurement you have 2 options.
1) Divide its mass by the density of its material (if you canfind that).
2) Use displacement in water - measure the volume of the water displaced by the board's total submersion in it, then use the relationship 1cubic metre = 1000 litres. (Or the corresponding cubic feet / gallon ratio.)
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It is not possible to calculate the area given only the volume.
You cannot calculate volume of surface area. If you meant 20m3, then the volume would be 20,000 litres.
Not enough information. To calculate mass, you would need volume and density (mass = volume x density).
Bulk density = dry weight / volume, then by knowing the dry weight and bulk density we can calculate the volume.
Partition (or divide) the irregular object into summation of regular objects and then calculate the volume.