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The answer depends on which area is shaded for each inequality. I always teach pupils to shade the unwanted or non-feasible region. That way the solution is in the unshaded area. This is much easier to identify than do distinguish between a region which is shaded three times and another which is shaded four times.
It is the way to calculate a given square's area. It is the definition of its area.
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.
The same way you calculate the surface area of any other rectangle: Multiply the length of the wall by its height.
Probably Heron wanted a way to calculate the area of the triangle.