Understand the idea.
Look inside a solid
A cross-section is the flat shape exposed by a cut through a solid. A prism has two matching, parallel polygon ends and a uniform shape along its length. Its side faces join corresponding edges of those ends.
A cut parallel to the matching ends has the same shape and size as an end. In the triangular prism shown, that section is a triangle. The rectangles on the outside are side faces, rather than this particular section.
State the cut direction
Read the cut direction before naming the cross-section. For a right prism, a cut parallel to the ends is perpendicular to its length. Moving that cut along the interior of the prism does not change the section’s shape or size.
A cut in another direction can produce a different section. Also separate the actual shape from its appearance in a perspective drawing: a rectangular face may be drawn slanting on the page while still having four right angles in the solid.
See the method in action.
A triangular section
A triangular prism is cut halfway along its length, parallel to its ends. Name the cross-section.
Worked solution
- 1
Identify the matching end faces.
The name triangular prism tells us that its two matching ends are triangles.
- 2
Use the direction of the cut.
A cut parallel to those ends passes through the same triangular shape at the halfway position.
- 3
Name the exposed shape.
A uniform prism has matching parallel sections all along its length.
A triangle.
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.
Worked solution
- 1
Match the section to an end face.
A cut parallel to the ends has the same shape and dimensions as an end.
- 2
Apply the rectangle area formula.
Area counts the square units inside this rectangular section.
- 3
State the section’s area.
Multiplying the two centimetre lengths produces square centimetres.
Rectangle; area 6 cm².
Try it yourself.
Check your understanding
A pentagonal prism is sliced parallel to its ends. How many sides does its section have?
Show answer & reasoning
5
A section parallel to the ends matches a pentagonal prism’s pentagonal end face. A pentagon has sides, so the section has sides.
Keep practising
6 worksheet questions · 10 marks
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.
.
- 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 ↗