The two ways are:
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find buoyancy and the height depth and with and you've got your answer
v=s.h where h:height and s:surfacev=m/d where m:mass and d:density
If it is a small shape that is denser than a convenient fluid and insoluble in it and also does not react with it then the displacement method is simplest. Fill a graduated cylinder with the fluid, measure the volume of the fluid. Then gently insert the shape and measure the apparent volume of the fluid. The difference between the two volume readings is the volume of the shape. If the shape is less dense than the fluid you have to make one change. You need to find a dense insoluble object. Measure the volume of the fluid with the dense object immersed in it. Then measure the volume when the dense object and the shape are joined together and submerged. The difference between the two measures is the volume of the shape. This method will not work with soluble shapes unless you can find a fluid that it is not soluble in. Similarly, you cannot use a fluid that will react. So measuring the volume of a lump of sugar or a lump of sodium using water are non-starters. Finally, the method will not work if the irregular shape is huge.
If a shape is two dimensional it has NO volume - volume is an attribute of THREE dimensional shapes.If you meant the AREA of an irregular two dimensional shape, then divided it up into areas which are not irregular and so you can calculates them, and sum the areas of these non-irregular shapes.If you meant the volume of an irregular THREE dimensional shape, then a similar process can be followed by dividing it up into three dimensional shapes you can can calculate the volume of and summing them, though if it is an irregular object that you are physically holding, then you can find its volume by finding the increase in volume of a liquid (In a regular container) when the object is submerged into that liquid.
An irregular volume is one that has no simple equation to describe it's shape. An example would be a cylinder with a cone on it's end. The shape can often be divided into two or more regular shapes which have known equations that describe them. In this case, a cylinder and a cone. To then find the total volume of the irregular shape, you sum the volumes of the individual regular shape volumes.