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For the triangles:
The orange triangle and the green triangle have different slopes. For the top shape, what looks like the hypotenuse of a triangle is actually changing from a lower slope to a steeper slope, resulting in a slightly concave shape. For the bottom shape, the opposite is true, and the shape is slightly convex. The convex shape takes up more area than the concave shape, but we have the same parts to cover that area with, so there is one square left empty.
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