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There is no such thing as an "irregular rectangle". To calculate the area of a rectangle - if that's what you mean - you multiply length x width.
For example, you can divide the polygon into triangles, and calculate the area of each triangle.
By integration, which basically means dividing the object into small pieces.
The most direct way to calculate the area of an irregular shape is to superimpose it on graph paper, and then count the number of complete squares that it covers, and for squares that are only partially covered, estimate how much of the square is covered to the nearest simple fraction (a half, a third etc.). If you want the surrounding area rather than the area of the shape itself, you could calculate the total area and then subtract the area of the shape.
Partition (or divide) the irregular object into summation of regular objects and then calculate the volume.