Nets that fold into solids
Draw and interpret nets, matching faces and lengths while checking for overlap.
Core and Extended.
Before you begin
- Recognise solid faces.
- Calculate rectangular and triangular areas.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the area of a 3 cm by 4 cm rectangle?
What you will learn
- Identify and draw nets of cubes, cuboids, prisms and pyramids.
- Match shared edges when folding.
- Use face dimensions to calculate a surface area.
A net opens every face
A net is a connected flat arrangement of all the faces of a solid that can fold without overlap. A cube needs six equal squares, but six squares in a strip will not form a cube: folding cannot create six distinct enclosing faces. Imagine folding around shared edges, or cut out a paper copy to check a doubtful arrangement.
In the illustrated cube net, four squares form a row and the remaining squares attach above and below the second square. That square can become the base; its neighbours rise around it and the far end closes the top. Tabs used for gluing are not faces and are excluded from surface area. Draw straight edges with a ruler and mark matching lengths.
Match the net to its cross-section
A cuboid net has three pairs of equal rectangles. For dimensions 3, 4 and 5 cm, the face pairs are 3 by 4, 3 by 5 and 4 by 5. A right triangular prism net has two congruent triangles and three rectangles whose widths match the three triangle sides; their other dimension is the prism's length.
A square-based pyramid net has one square with four triangles, each triangle's base matching a square side. The triangle's perpendicular face height is a sloping measurement on the solid, not necessarily the pyramid's vertical height. To find surface area from a net, add the areas of every face once. The net reveals boundaries; calculating volumes is developed in Mensuration.
Pause and explain
A square-based pyramid net has which faces?
Worked example
A closed cuboid has sides 3 cm, 4 cm and 5 cm. Describe its net and calculate the total area of its faces.
Show the worked solution
- Use two 3 × 4 rectangles, two 3 × 5 rectangles and two 4 × 5 rectangles.
- Their areas are 12, 15 and 20 cm² for one of each pair.
- Double the sum: 2(12 + 15 + 20) = 94 cm².
Answer Six matched rectangles; total face area 94 cm².
From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Draw the illustrated cube net with each square side 2 cm. Find its face area.
Give me a hint
Draw six equal squares with matching fold edges.
Compare my reasoning
- Draw four 2 cm squares in a row, adding one above and one below the second.
- Each face has area 2 × 2 = 4 cm².
- All six faces give 6 × 4 = 24 cm²; exclude any glue tabs.
A valid cross-shaped net; 24 cm².
Look for these in your work
- Drew six equal faces with a ruler.
- Counted each face once.
Sketch a net for a right triangular prism with a 3–4–5 cm triangular cross-section and length 8 cm. Find its surface area.
Give me a hint
Use two right triangles and rectangles of widths 3, 4 and 5.
Compare my reasoning
- The two triangular faces total 2 × (3 × 4 ÷ 2) = 12 cm².
- The rectangular faces total 8(3 + 4 + 5) = 96 cm².
- Adding all five faces gives 108 cm²; match the triangle edges to rectangle widths.
Two 3–4–5 triangles and 3×8, 4×8, 5×8 rectangles; 108 cm².
Look for these in your work
- Matched all three cross-section edges.
- Included both end faces.
A pyramid has a 6 cm square base and four triangular faces, each with perpendicular face height 5 cm. How much card covers the closed solid, excluding tabs?
Give me a hint
Use the face height given, not a vertical solid height.
Compare my reasoning
- The square base area is 6 × 6 = 36 cm².
- Each triangle area is 6 × 5 ÷ 2 = 15 cm²; four total 60 cm².
- The closed net needs 36 + 60 = 96 cm².
96 cm².
Look for these in your work
- Used perpendicular height for each triangular face.
- Included the base and all four sides.
Common mistakes
- Accepting a net from face count alone.
- Leaving out a closed solid's base or end face.
- Confusing a triangle's face height with the pyramid's vertical height.
What can you explain now?
Is every connected arrangement of six equal squares a cube net?
Compare with the explanation
No.
The faces must fold into six distinct enclosing positions without overlap; being connected and having six squares is insufficient.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, draw a cuboid net and label its three pairs of equal rectangles. Fold a paper copy to check your arrangement.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.
Original StudyForA teaching content · AI-assisted checks · Human teacher review pending.
Number contains 19 sequenced lessons; Algebra and graphs 21; Coordinate geometry 10; Geometry 15; Mensuration 13; Trigonometry 13; Transformations and vectors 11; Probability 7; Statistics 13. All 72 syllabus section entries now link to teaching and staged practice. Seven mixed checkpoints sample skills and suggest review lessons. Nine earlier overviews remain available. Full cumulative assessment and human teacher review remain pending. Written lesson practice, charts and constructions are self-checked, not automatically graded. Checkpoints do not save an exam grade or certify mastery.
Check the official syllabus 2025–2027 Open related practice and resources