As shown in the picture, on a rectangular grassland 80 meters long and 40 meters wide, there is a curved stone path to calculate the area of grassland (the horizontal width of the path is 1 meter anywhere)

As shown in the picture, on a rectangular grassland 80 meters long and 40 meters wide, there is a curved stone path to calculate the area of grassland (the horizontal width of the path is 1 meter anywhere)

Area = (80-1) × (40-1) = 3081 square meters;
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As shown in Figure 4, on a rectangular lawn, there is a curved asphalt path (the horizontal width of any part of the path is 1 unit). Please guess the empty path

Suppose we cut off the path, translate the left grassland and connect it with the right grassland to form a new rectangle, so the rectangle is (A-1) long and B wide, so the area is (A-1) B, that is (ab-b), which is the area of the blank part

As shown in the picture, on a rectangular grassland, there is a curved asphalt path (the horizontal width of the path is 1 unit everywhere). Please guess what the grassland area is represented by the blank part? And explain that your conjecture is correct

Moving the path to the left to the edge, we can get the length of the rectangular grassland of the blank part as B-1, so the grassland area represented by the blank part = B (A-1) = ab-b