Final answer:
If a shape can be decomposed to completely cover another shape, without gaps or overlaps, they will have the same area.
Step-by-step explanation:
The statement is true.
If a shape can be decomposed so that it covers another shape exactly with no gaps or overlaps, the two shapes will have the same area. This is because when the shape is decomposed, the pieces can be rearranged to form the other shape without changing the overall area. For example, if a rectangle is decomposed into smaller rectangles and rearranged to form a square, the total area of the rectangles will be the same as the area of the square.
Therefore, if two shapes can be decomposed and cover each other without gaps or overlaps, they will have the same area.