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.
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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".
A regular shape such as a square or rectangle - length times width. If it is an irregular shape, fit known sized squares and triangles within the shape's border and work out area of a square and a triangle times the number of squares and triangles.
You break it up into smaller shapes which are less irregular. If these are more regular, you can calculate their contribution to the perimeter, and their area. You can then add these together.
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.
You approximate the irregular shape with many small regular figure, for example, long and thin rectangles.