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You approximate your irregular figure lots of small figures of known shapes. For example, you can divide it into lots of thin vertical (or horizontal) stripes, each of which is approximately a rectangle.
You divide the shape into smaller shapes you can calculate, like rectangles and triangles. If the shape is irregular, you have to approximate, for example by dividing it into many narrow rectangles. This technique is called "integration".
You approximate the irregular shape with many small regular figure, for example, long and thin rectangles.
You get the area by using formulas. There is usually a specific formula to find the area of each shape. Some irregular shaps may not have a formula.
There is no standard formula. It is necessary to partition the irregular hexagon into more convenient shapes such as triangles and quadrilaterals, find their areas and sum the results.