Skill: Identify cross-sections of solids informally

A cross-section is the 2D shape you see when a flat plane “slices” through a 3D solid.

To identify it:

1. Imagine where the flat cut goes.
2. Notice whether the cut is parallel or perpendicular to a face or base.
3. Identify the 2D shape made by the cut.
4. Remember that the cross-section is the shape of the slice, not necessarily one of the solid’s existing faces.

Example: A rectangular prism is $6$ units long, $4$ units wide, and $3$ units tall. A plane cuts through the prism halfway up, parallel to its bottom and top faces. What shape is the cross-section?

1. The plane is parallel to the bottom of the prism.
2. A bottom face of a rectangular prism is a rectangle measuring $6$ units by $4$ units.
3. A slice parallel to the bottom has the same shape and dimensions as the bottom face.
4. Therefore, the cross-section is a rectangle:

$$6\text{ units} \times 4\text{ units}$$

Because the cut is halfway up the prism, this rectangle is a new slice through the interior. It is not one of the prism’s original faces.

The cross-section would change if the plane’s direction changed. For example, a vertical cut could make a different rectangle.