How to know what type of cross section is it going to be?

Question

A plane intersects a right rectangular pyramid. Producing a cross section. The plane is parallel to the base. What shape is the cross section?

I thought it would be triangle cause triangle cut is going to be triangle right? Also I don't really understand what cross section is? How do i do these types of question?

Answer 1

Hint: A cross section is the shape that arises in the intersection of a plane and any solid. For example, if you cut a sphere in half, you will get a circle on the side you cut. The circle is the cross section of the sphere.

These gifs will visualize various cross sections of a cube, I hope:

Answer 2

Hint:

You cut the pyramid with a knife, horizontallly at height $z \le h$, what shape is the cut part that remains if the top is removed? Or in other words: what is the intersection, the set of common points, of cutting plane and pyramid? If $h$ is the height of the pyramid, how does that intersection, here refered as cross section, look for different $z$, e.g $z \in \{ 1/2, h, 0, 2h, -1 \}$?

Algebraicly one can describe the cutting plane by an equation $z = c$ for some constant.

The points $(x,y,z)$ that make up the square pyramid with base length $b$ and height $h$, with its base centered at the origin, can be written as $$ \lvert x \rvert + (b/(2h)) z \le b/2 \\ \lvert y \rvert + (b/(2h)) z \le b/2 \\ $$ Intersection means the equations for plane and pyramid must hold simultaneously, giving the conditions for the coordinates of the points of the cross section surface.