math class 678 4-in-1 skill sheets
7.G.A.3 7th Grade Geometry

Cross-Sections of 3D Figures

Describe the two-dimensional figures that result from slicing three-dimensional figures, such as plane sections of right prisms and pyramids.

How to explain it

At this standard, students describe and identify the two-dimensional shape that results when a plane slices a three-dimensional figure, distinguishing how horizontal, vertical, and angled cuts produce different cross-sections.

The anchor students hold onto: A cross-section is the 2D face exposed by a slice. Horizontal cut (parallel to base) usually matches the base shape. Vertical cut (perpendicular to base) often gives a different shape.

Visualizing cross-sections builds the spatial reasoning students use in 8.G.C.9 for the volume of cylinders, cones, and spheres, and in high school geometry for solids of revolution.

Worked examples

Example 1 Prism, Horizontal
Prism, horizontal slice
Step 1A right rectangular prism is cut parallel to its base.
Step 2The slice exposes a face the same shape as the base.
Step 3The base is a rectangle, so the cross-section is a rectangle.
AnswerRectangle
Example 2 Pyramid, Vertical
Pyramid, vertical slice
Step 1A rectangular pyramid is cut down through its apex.
Step 2The slice runs from the top point to the base.
Step 3It exposes a triangle: point on top, base below.
AnswerTriangle

Common mistakes

What students write Believing every cross-section of a solid is the same as its base, no matter how it is cut.
The fix The cut DIRECTION matters. A vertical slice of a cylinder is a rectangle, not a circle. A vertical slice of a rectangular pyramid is a triangle, not a rectangle. Always check horizontal vs vertical first.
Try this A cylinder is sliced vertically, straight down through its side. Rivera says: "The cross-section is a circle, because a cylinder has circles." Identify Rivera’s error and name the correct cross-section.
What students write Confusing the 3D solid with the 2D cross-section — naming the solid instead of the slice shape.
The fix A cross-section is always a flat 2D shape: rectangle, triangle, circle, square, or trapezoid. Never answer "cylinder" or "pyramid" — those are the solids, not the slices.
Try this A rectangular pyramid is sliced vertically through its apex. Tran says: "The cross-section is a rectangle, because the base is a rectangle." Identify Tran’s error and name the correct cross-section.

Teacher tip

Head off the two predictable errors before they happen. First: The cut DIRECTION matters. A vertical slice of a cylinder is a rectangle, not a circle. A vertical slice of a rectangular pyramid is a triangle, not a rectangle. Always check horizontal vs vertical first. Second: A cross-section is always a flat 2D shape: rectangle, triangle, circle, square, or trapezoid. Never answer "cylinder" or "pyramid" — those are the solids, not the slices.