Question

a rectangular prism and rectangular pyramid are shown.
statements are given about the shape of the cross - section that would result from slicing the figures in different ways.
determine whether each statement about the resulting cross - section matches one or both of the figures shown.

	rectangular prism	rectangular pyramid
the cross - section for a slice parallel to the base would be congruent to the base.	✔	☐
the cross - section for slice parallel or perpendicular to the base could result in a shape with 4 sides.	✔	✔

Explanation:

Step1: Analyze Rectangular Prism Cross - Section (Parallel to Base)

For a rectangular prism, when we slice it parallel to the base, the cross - section is a rectangle (same shape as the rectangular base) and congruent to the base because the prism has uniform cross - sections along its height.

Step2: Analyze Rectangular Pyramid Cross - Section (Parallel to Base)

For a rectangular pyramid, when we slice it parallel to the base, the cross - section is a rectangle (same shape as the rectangular base) but it is not congruent to the base. As we move up the pyramid, the cross - section gets smaller, so the area is less and the sides are shorter.

Step3: Analyze 4 - Sided Cross - Sections

• For the rectangular prism: Slicing parallel or perpendicular to the base (which is a rectangle) will result in a quadrilateral (4 - sided figure). For example, a parallel slice is a rectangle, a perpendicular slice (along the height and parallel to an edge) is also a rectangle.
• For the rectangular pyramid: Slicing parallel to the base gives a rectangle (4 - sided). Slicing perpendicular to the base (through the apex and a side of the base) gives a triangle, but slicing perpendicular to the base and parallel to a pair of opposite sides of the base can give a trapezoid (which is 4 - sided) or a rectangle in some cases. So both can have 4 - sided cross - sections when sliced parallel or (in the case of the prism, always; in the case of the pyramid, in some cases) perpendicular to the base.

Answer:

• "The cross - section for a slice parallel to the base would be the same shape as the base." - Matches both (Rectangular Prism and Rectangular Pyramid) as both have rectangular bases and a parallel slice gives a rectangle (same shape as base).
• "The cross - section for a slice parallel to the base would be congruent to the base." - Matches only the Rectangular Prism (since the pyramid's parallel slice is similar but not congruent).
• "The cross - section for slice parallel or perpendicular to the base could result in a shape with 4 sides." - Matches both (Prism always has 4 - sided cross - sections in such slices, Pyramid can have 4 - sided cross - sections in parallel or some perpendicular slices).