Final answer:
The shape formed by the intersection of the box with the lid of a hexagonal prism is a hexagon.
Step-by-step explanation:
The hexagonal prism is a three-dimensional geometric shape with six rectangular faces and two hexagonal faces—one at the top and one at the bottom. The lid, which is a flat piece of cardboard, completely covers the top hexagonal face of the hexagonal prism. When the lid is placed on top, it intersects with the box, forming a hexagon. This hexagon is a two-dimensional shape resulting from the intersection of the prism and the lid. It is bounded by six straight sides, forming a closed polygon. The hexagon represents the cross-section of the hexagonal prism formed when the lid covers its top face.