Question

a right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid. what is the shape of the cross - section?
a. trapezoid
b. pyramid
c. triangle
d. square

Explanation:

Step1: Analyze cross - section of pyramid

When a right rectangular pyramid is sliced vertically (down) by a plane not passing through the vertex, consider the properties of the intersection.
A trapezoid has one pair of parallel sides. In the case of the pyramid slice:
The base of the pyramid is a rectangle (for a right rectangular pyramid). The non - parallel sides are formed by the slant edges of the pyramid. The plane cuts through two non - adjacent lateral faces and the base. One pair of sides of the cross - section is parallel (the side parallel to a side of the base rectangle) and the other pair is not.

Step2: Eliminate other options

• Option B: A pyramid is a 3 - D shape, not a 2 - D cross - section.
• Option C: A triangle is formed when the plane passes through the vertex (since then it would intersect three faces: two lateral and the base).
• Option D: A square would require all sides to be equal and parallel in a specific way. But in a non - vertex - passing vertical slice of a right rectangular pyramid (where the base is a rectangle, not necessarily a square), all sides of the cross - section won't be equal and parallel as required for a square.

Answer:

A. Trapezoid