Square
Divide a square int into four identical squares. Remove the bottom right hand square.
Divide the resulting shape into four identical shapes.
Triangle
Divide an equilateral into four identical shapes. Remove the bottom right hand shape.
Divide the resulting shape into four identical shapes.
Note that in both the square and triangle case, we can divide the remaining 3 shapes again into 4 parts. We need to pick 3 of the smaller parts to make the new identical shape. If we pick the part from each of the 3 shapes that are next to each other, we automatically get the required shape.