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You could consider the cross as two intersecting rectangles. Calculate the area of both rectangles and the area of the intersection (overlap). Then area of cross = sum of the areas of the rectangles minus the area of the overlap.
To find the different rectangles with an area of 32 square units, we need to consider the factor pairs of 32. The pairs are (1, 32), (2, 16), (4, 8), and their reverses, giving us the dimensions of the rectangles: 1x32, 2x16, 4x8, and 8x4. However, since the order of dimensions does not create a new rectangle, we have four unique rectangles: 1x32, 2x16, and 4x8. Thus, there are three distinct rectangles with an area of 32 square units.
In a 4 by 4 grid, there are 16 squares (1x1 squares), 9 rectangles that are 2x1, 6 rectangles that are 3x1, 4 rectangles that are 2x2, and 1 rectangle that is 4x4. Therefore, in total, there are 16 squares and 20 rectangles in a 4 by 4 grid.
16
When rectangles are inscribed, they lie entirely inside the area you're calculating. They never cross over the curve that bounds the area. Circumscribed rectangles cross over the curve and lie partially outside of the area. Circumscribed rectangles always yield a larger area than inscribed rectangles.