Question

identifying cross sections of solids
use the diagram to answer the questions.
what two - dimensional figure will be created by a horizontal cross section?
what two - dimensional figure will be created by a vertical cross section through the apex?

Explanation:

For the first question (horizontal cross - section):

Step1: Analyze the solid

The given solid is a pyramid with a pentagonal base (a pentagonal pyramid). When we take a horizontal cross - section (a cut parallel to the base) of a pyramid, the cross - section will be similar to the base of the pyramid.

Step2: Determine the shape of the cross - section

Since the base of the pyramid is a pentagon, a horizontal cross - section (parallel to the base) will also be a pentagon.

For the second question (vertical cross - section through the apex):

Step1: Analyze the vertical cut through the apex

A vertical cross - section through the apex of a pyramid will pass through the apex and two opposite vertices (or edges) of the base. In the case of a pentagonal pyramid, when we make a vertical cut through the apex, the cross - section will be a triangle. This is because the two sides of the cross - section from the apex to the base will form the two equal (or proportional) sides of a triangle, and the base of the triangle will be a side of the pentagonal base (or a line segment connecting two points on the base).

Answer:

For the horizontal cross - section: Pentagon
For the vertical cross - section through the apex: Triangle