A square pyramid with base side 3 cm and height 6 cm is sliced by a plane parallel to the square base. What 2D cross-section is formed?
Show reasoning / computation: __________________________________________
CCSS 7.G.A.3 · plane sections of 3D figures
Cross Sections of 3D Figures Worksheet Generator
Read a schematic solid and slice direction, then identify the 2D figure made by the plane. The diagrams are intentionally schematic and labeled so students reason from the cut, not from misleading perspective distortion.
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Cross Sections of 3D Figures
Diagrams are part of the problem data, not decorative assets. Student pages keep solution-specific marks hidden; reveal answers or use the separate PDF key to check work.
Problem 1
Problem 2
A triangular prism with a triangular base 5 cm wide and 8 cm high and prism length 10 cm is sliced by a plane perpendicular to the triangular bases and parallel to the prism length. What 2D cross-section is formed?
Show reasoning / computation: __________________________________________
Problem 3
A rectangular prism measuring 6 cm by 8 cm by 11 cm is sliced by a plane parallel to the rectangular base. What 2D cross-section is formed?
Show reasoning / computation: __________________________________________
Problem 4
A cube with side length 5 cm is sliced by a plane parallel to one face. What 2D cross-section is formed?
Show reasoning / computation: __________________________________________
Problem 5
A triangular prism with a triangular base 5 cm wide and 3 cm high and prism length 9 cm is sliced by a plane perpendicular to the triangular bases and parallel to the prism length. What 2D cross-section is formed?
Show reasoning / computation: __________________________________________
Problem 6
A triangular prism with a triangular base 9 cm wide and 7 cm high and prism length 10 cm is sliced by a plane perpendicular to the triangular bases and parallel to the prism length. What 2D cross-section is formed?
Show reasoning / computation: __________________________________________
Problem 7
A rectangular prism measuring 6 cm by 9 cm by 11 cm is sliced by a plane perpendicular to the base and parallel to a side face. What 2D cross-section is formed?
Show reasoning / computation: __________________________________________
Problem 8
A triangular prism with a triangular base 8 cm wide and 3 cm high and prism length 8 cm is sliced by a plane perpendicular to the triangular bases and parallel to the prism length. What 2D cross-section is formed?
Show reasoning / computation: __________________________________________
Describing a cross-section of a solid figure
A cross-section is the flat shape you see when a plane slices through a solid. The shape depends on the solid and the angle of the cut. Slicing parallel to a base gives a shape like the base, and slicing perpendicular to the base through a prism or cylinder gives a rectangle.
Worked examples
- A rectangular prism cut parallel to its base gives a rectangle the same size as the base.
- A cylinder cut parallel to its bases gives a circle, and cut perpendicular to the bases through its axis gives a rectangle.
- A square pyramid cut parallel to its base gives a smaller square.
Common slips
- Thinking every slice of a pyramid is a triangle. A cut parallel to the base gives a square, and a cut through the peak gives a triangle.
- Confusing a cross-section with a net. A net unfolds the surface, but a cross-section is a slice through the inside.
- Ignoring the angle of the cut, which changes the shape.
How to use this worksheet
Ask students to describe the plane's position (parallel or perpendicular to the base) before naming the shape. The answer key names the cross-section for each cut.
Common Core connection
- 7.G.A.3 · Describe two-dimensional cross-sections formed by slicing three-dimensional figures.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Classroom note 1
A plane parallel to a prism base produces a cross-section congruent to that base.
Classroom note 2
A plane through a pyramid apex and across the base can produce a triangle.
Classroom note 3
Example: slicing a rectangular prism parallel to its base gives a rectangle congruent to that base, while an angled slice can give a larger rectangle or another quadrilateral.
Classroom note 4
Perspective drawings are schematic; use the stated slice direction as the mathematical condition.
Continue the 7.G progression
Move to another Grade 7 geometry skill
Questions people ask
Are the 3D drawings to scale?
No. Perspective solids are marked and treated as schematics; the slice relationship, not apparent screen length, determines the answer.
Which solids appear?
Current seeds include rectangular prisms, triangular prisms, square pyramids, and cubes.
Which standard does this practice?
CCSS 7.G.A.3: describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and pyramids.