Cross-Sections of 3D Figures Math Example 3

Solution

1. 1
   Step 1: A regular hexagonal prism has two parallel regular hexagon bases connected by rectangular lateral faces. The plane is perpendicular to both bases (vertical cut).
2. 2
   Step 2: The plane passes through two opposite edges of each hexagonal base. In a regular hexagon, opposite edges are parallel and separated by a distance equal to $s\sqrt{3}$ (where $s$ is the side length). The plane intersects the top base along a segment connecting two opposite edges and the bottom base along a corresponding segment.
3. 3
   Step 3: Since the cutting plane is perpendicular to the bases, the cross-section has two horizontal edges (one on each base) and two vertical edges (along the lateral faces). The top and bottom edges have equal length, and the vertical edges equal the prism's height $h$.
4. 4
   Step 4: The cross-section is a rectangle with width equal to the distance between opposite edges of the hexagon ($s\sqrt{3}$) and height equal to $h$.