Rearrangement of areas

Rearrangement of areas is the process of decomposing a geometric figure into finitely many pieces and rearranging them (using translations, rotations, or reflections) to form another figure. The total area remains unchanged, as area is preserved under these movements.

Important properties

• Cutting a shape into pieces and rearranging them does not change the total area.

• If two shapes can be rearranged into each other using only cutting and moving, they have equal areas.

• This principle is used to prove area formulas and solve geometric puzzles.