Question

A cross section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base. The cross section can be which of these shapes? Check all that apply. square triangle trapezoid circle non-square rectangle

Answer 1

A cross section parallel to the base will be a square.

One perpendicular to the base will be a trapezoid, or if it passes through the vertex of the pyramid, a triangle.

Answer 2

Square, Triangle and Trapezoid

Explanation:

We know that,

Square pyramid is a pyramid having a square base and there are two types of square pyramids as shown below by figure 1 and 2.

Now, it is given that the plane intersects the pyramid with angle either perpendicular or parallel to the base.

1. If the plane is parallel to the base of either of the pyramids.

Then, we see that the cross-section shape for both figures will be a square.

2. If the plane is perpendicular to the base of either of the pyramids.

We see that,

In figure 1, the cross-section shape will be a triangle.

In figure 2, the cross-section shape will be a trapezoid.

Hence, the correct cross-section shapes are given by,

Square

Triangle

Trapezoid