The idea, step by step
Look inside a solid
A cross-section is the flat shape exposed by a cut through a solid. A prism has matching, parallel polygon ends joined by flat side faces. Its shape stays uniform along its length.
For a cut at right angles to a prism’s length, the section matches an end face. The triangular prism shown has a triangular section, not a rectangle merely because some side faces are rectangles.
State the cut direction
The direction of the cut matters. “Parallel to the end faces” means the same direction as those matching ends; this is perpendicular to the prism’s length. Such cuts have the same shape and size wherever they are made inside a uniform prism.
A slanted cut can give a different section. Always read the stated cut direction before naming a shape. A diagram is a representation of a solid, so a rectangle may look like a parallelogram in the drawing.
A common trap
Naming a visible side face instead of the section produced by the stated cut.
Instead: Identify the matching end faces and check whether the cut is parallel to them.
See the thinking
A triangular section
A triangular prism is cut halfway along its length, parallel to its ends. Name the cross-section.
- The matching end faces are triangles.
- A parallel cut through this uniform prism matches those ends.
Section size
A rectangular prism has end faces 3 cm wide and 2 cm high. A cut is made parallel to those ends. Find the section’s shape and area.
- The section is a matching rectangle, 3 cm by 2 cm.
- Rectangle area = 3 × 2 = 6 cm².
Check your understanding
A pentagonal prism is sliced parallel to its ends. How many sides does its section have?
Show answer
5
The section is a pentagon, matching the end faces.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- A triangular prism is cut parallel to its end faces. Name and sketch the section.2 marks
- A pentagonal prism is cut perpendicular to its length. How many sides does the section have?1 mark
- A rectangular prism is cut parallel to its rectangular ends. Name the section.1 mark
- The end of a prism is a rectangle 4 cm by 2 cm. A parallel section is cut. Find its area.2 marks
- A student says every possible cut through a rectangular prism must show a rectangle. Is that guaranteed? Explain.2 marks
- A prism has matching hexagonal ends. Draw the shape of a section parallel to the ends and state its number of sides.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A triangular prism is cut parallel to its end faces. Name and sketch the section.2 marks
The cross-section matches the triangular ends.
A triangle. - A pentagonal prism is cut perpendicular to its length. How many sides does the section have?1 mark
The section matches a pentagonal end face.
5 sides - A rectangular prism is cut parallel to its rectangular ends. Name the section.1 mark
Parallel sections of a uniform prism match its ends.
A rectangle. - The end of a prism is a rectangle 4 cm by 2 cm. A parallel section is cut. Find its area.2 marks
The section has the same dimensions as the end.
4 × 2 = 8 cm².
8 cm² - A student says every possible cut through a rectangular prism must show a rectangle. Is that guaranteed? Explain.2 marks
A cut parallel to a rectangular end gives a rectangle.
A slanted cut is not guaranteed to have that same shape.
No. The direction of the cut matters. - A prism has matching hexagonal ends. Draw the shape of a section parallel to the ends and state its number of sides.2 marks
The section matches an end face.
A hexagon with 6 sides.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 6 prism cross-sections, combined transformations and tessellations, with visual reasoning.
Official curriculum source ↗