Question

Ryan is replacing the ornamental pyramids on top of the fence posts surrounding his yard. They’ve weathered over time. He starts with a block in the shape of a pyramid with a square base. He plans to slice a few inches off its top and sides to make the post toppers safe for his children to play around. In this activity, you’ll look at the cross sections of the pyramid cut by a number of planes in different orientations. Part A Ryan slices off the top of the pyramid and gets a cross section parallel to the base. What is the shape of this cross section?

Answer 1

the shape of the cross section is square

Answer 2

Slicing off the top of a pyramid such that the cross section is parallel to the base of the pyramid gives the same shape as the shape of the base of the pyramid.

Given a block in the shape of a pyramid with a square base, a slice off the top of the pyramid to get a cross section parrallel to the base will result in the shape of the cross section being equivalent to the shape of the base of the pyramid.

Therefore, the shape of the cross section is a square.