an image of a rectangular pyramid is shown below:

part a: a cross section of the rectangular pyramid is cut with a plane parallel to the base. what is the name of the shape created by the cross section? explain your answer.

part b: if a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex, what would be the shape of the resulting cross section? explain your answer.

A cross section (for 3 dimensional figures) is a 2 dimensional object that is essentially added up to get the figure. In this case, when we cut a horizontal line within the prism, we end up with a rectangle (hence the name rectangular prism). Credits to https://www.mathsisfun.com/geometry/images/pyramid-cross-section.svg for some help with this. 

If it was perpendicular to the base, we'll have to note that the shape has a point with a base that is part of the rectangular base, making a triangle