a pentagonal prism is cut by a plane perpendicular to the base. what is the shape of the cross section that…

a pentagonal prism is cut by a plane perpendicular to the base. what is the shape of the cross section that is formed?\n\na. a pentagon with one pair of equal sides\n\nb. a trapezoid with one pair of parallel sides\n\nc. a rectangle\n\nd. a triangle\n\ne. a hexagon

a pentagonal prism is cut by a plane perpendicular to the base. what is the shape of the cross section that is formed?\n\na. a pentagon with one pair of equal sides\n\nb. a trapezoid with one pair of parallel sides\n\nc. a rectangle\n\nd. a triangle\n\ne. a hexagon

Answer

Explanation:

Step1: Recall Prism Properties

A pentagonal prism has two pentagonal bases and five rectangular lateral faces, with lateral edges perpendicular to the bases.

Step2: Analyze Plane Cut

A plane perpendicular to the base will intersect the prism. Since the lateral edges are perpendicular to the base, the intersection with the lateral faces will be vertical (parallel to lateral edges) and the intersection with the base (or top) will be horizontal. The cross - section will have four right angles (because the plane is perpendicular to the base and the lateral edges are perpendicular to the base, so the sides of the cross - section formed by the intersection with the lateral faces and the base/top will be perpendicular) and opposite sides parallel. This is the definition of a rectangle. Let's analyze other options:

  • Option A: A pentagonal prism cut perpendicular to the base will not form a pentagon with one pair of equal sides. The cross - section should have four sides (from the intersection with the lateral faces and the two bases) not five.
  • Option B: A trapezoid has only one pair of parallel sides, but our cross - section has two pairs of parallel sides (since it's a rectangle), so it's not a trapezoid.
  • Option D: A triangle has three sides, but our cross - section is formed by intersecting the prism with a plane perpendicular to the base, which will result in a four - sided figure, not a triangle.
  • Option E: A hexagon has six sides, and our cross - section will have four sides, so it's not a hexagon.

Answer:

C. a rectangle