Question

what shape will result from taking a cross section of the rectangular prism through the points shown?
what shape will result from taking a cross section of the rectangular prism through the points shown?

Explanation:

Analyze the first rectangular prism

• Three points are given: one on the top-back edge, and two on the bottom-front edge.
• A plane passing through these three points cuts diagonally through the prism.
• The intersection of this plane with the faces of the rectangular prism forms a 4-sided polygon where opposite sides are parallel, specifically a rectangle.

Analyze the second rectangular prism

• Three points are given: one on the top-left-back edge, one on the front-left vertical edge, and one on the top-front edge.
• A plane passing through these three points cuts off a corner of the rectangular prism.
• The intersection of this plane with the three adjacent faces meeting at that corner forms a 3-sided polygon, which is a triangle.

Answer:

Question 1

Rectangle

Question 2

Triangle