Find the area of the black region

Shift the black region so that there is no gap within the figure and having a common base as above. Then the area of the black region is $64 \times 8 + 56 \times 20 + 28 \times 12 + 16 \times 8 = \boxed{2096}$ .

Using inclusion-exclusion, the area is the sum of the areas of the four larger rectangles (48x16, 12x40, 20x56, and 8x64) less the sum of the four distinct intersections of pairs of large rectangles (16x8, 12x8, 16x20, and 12x20). 2880 - 784 = 2096