In figure 1 the area of the square is 64 square units. In figure 2 the shapes are rearranged to form a rectangle ith an area of 65 square units. How do you justify the extra one squre unit?
Jenny, what you're describing is called a Tangram Vanishing Piece Puzzle.
You can find a discussion (solution) of them here: https://www.archimedes-lab.org/workshoptangram3.html
thank you so much!