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Nets

FoundationChallengeAQAEdexcelOCR

Master nets for GCSE Maths with structured, exam-style practice. This Foundation resource covers drawing and recognising nets of 3D shapes and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. A net folds up into the solid — check every face is included.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

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Stretch yourself beyond the basics.

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Topic overview

A net is a two-dimensional shape that folds up to make a three-dimensional solid. It shows every face laid out flat and joined along the edges.

A cube's net has six squares, and there are eleven different arrangements that fold correctly. Many arrangements of six squares do not work, so the test is whether the faces would overlap when folded.

Nets are useful for surface area, because the total area of the net equals the surface area of the solid. Drawing or imagining the net turns a three-dimensional problem into a two-dimensional one.

Revision notes

What makes a valid net

Every face must appear exactly once, joined along edges, and no two faces may overlap when folded.

Six squares in a row does not fold into a cube, because the ends would overlap. Mentally folding one face at a time is the reliable check.

Nets of common solids

A cube's net has six squares. A triangular prism's has two triangles and three rectangles.

A square-based pyramid's net has one square and four triangles. Matching the net's pieces to the solid's faces confirms it is correct.

Using nets for surface area

The area of the net is the surface area of the solid.

For a cube of side \(4\)cm, the net has six squares each \(16\)cm², giving \(96\)cm² in total.

Key points

  • A net folds up to form a 3D solid.
  • Every face appears exactly once.
  • Faces must not overlap when folded.
  • A cube's net has six squares.
  • There are eleven valid nets for a cube.
  • The area of the net equals the surface area.

Worked examples

Example 1

How many squares are in the net of a cube?

Working

\[\text{A cube has 6 faces}\]each face becomes one square
\[6 \text{ squares}\]state the answer

Example 2

Describe the net of a triangular prism.

Working

\[2 \text{ triangles}\]the two identical ends
\[3 \text{ rectangles}\]the three connecting faces

Example 3

Find the surface area of a cube of side \(5\)cm using its net.

Working

\[5 \times 5 = 25\text{cm}^2\]find the area of one square face
\[25 \times 6\]the net has six identical faces
\[= 150\text{cm}^2\]state the surface area

Common mistakes

  • Assuming any six squares form a cube net.

    Only eleven arrangements fold correctly; the rest cause overlapping faces.

  • Missing a face from the net.

    Every face of the solid must appear exactly once.

  • Using ordinary units for the net's area.

    Area is always in squared units.

  • Drawing faces that overlap when folded.

    Mentally fold each face to check the net works.

Exam tips

  • Count the faces of the solid first, then match them to the net.
  • Mentally fold the net one face at a time to check it works.
  • Use the net to find surface area — it turns 3D into 2D.
  • Include squared units for any area.

Key terms

Net
A flat shape that folds into a solid.
Face
A flat surface of a solid.
Surface area
The total area of all faces.
Fold
To bend a net along its edges to form the solid.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.