Question

what shapes can you create by taking cross sections of a cube?

a triangle
a pentagon
a hexagon
a trapezoid
an octagon

Explanation:

Determine possible cross-sectional shapes of a cube

A plane intersecting a cube can intersect at most 6 faces, meaning the resulting cross section can be a polygon with 3, 4, 5, or 6 sides.

Evaluate each given option

• a triangle: Created by slicing through three adjacent faces sharing a single vertex.
• a pentagon: Created by slicing through five of the six faces.
• a hexagon: Created by slicing through all six faces (e.g., a regular hexagon is formed by a plane passing through the midpoints of six edges).
• a trapezoid: Created by slicing through four faces where two of the intersecting faces are parallel (such as the top and bottom faces) and the slice is angled.
• an octagon: Impossible, as a cube only has 6 faces, so a plane can intersect at most 6 faces to form at most a 6-sided polygon (hexagon).

Answer:

• [x] a triangle (Correct answer)
• [x] a pentagon (Correct answer)
• [x] a hexagon (Correct answer)
• [x] a trapezoid (Correct answer)
• [ ] an octagon