Key takeaway: A net of a 3D figure is a flat pattern of connected polygons that folds along its edges to form the solid with no gaps and no overlaps.
Grade 66.G.A.4Geometry and Measurement
Definition of Net
A net of a 3D figure is what you get if you cut along some edges of a solid and unfold its surface flat. Every face of the solid appears exactly once, and faces that shared an edge stay joined along that edge.
A box has six rectangular faces, so its net has six rectangles. Many different arrangements work, and a single solid can have several correct nets, such as the cross shape or a long staircase. A pattern is a net only if folding it closes the surface without leaving a hole and without stacking two faces on the same spot. Nets are used by package designers, because the flat shape is what a machine actually cuts.
Notation
Each face in the net is a polygon labeled with its dimensions. For a box with dimensions 5 by 3 by 2, the six rectangles come in three matching pairs:
| Pair | Size | Count |
|---|---|---|
| Top and bottom | 5 by 3 | 2 |
| Front and back | 5 by 2 | 2 |
| Left and right | 3 by 2 | 2 |
Key facts
- The total area of a net of a 3D figure equals the surface area of the solid it folds into.
- A net must contain every face of the solid exactly once.
- Edges that will meet after folding must have equal lengths.
- One solid can have many different nets with the same pieces.
Net example
A cross-shaped net folds into a box that is 5 cm long, 3 cm wide and 2 cm tall. How many square centimeters of cardboard does the net use?
-
Top and bottom: \(2 \times (5 \times 3) = 30\).
-
Front and back: \(2 \times (5 \times 2) = 20\).
-
Left and right: \(2 \times (3 \times 2) = 12\).
-
Add the pieces: \(30 + 20 + 12 = 62\).
The net uses 62 square centimeters of cardboard.
Common mistake
Watch out
Gus draws six squares in one straight row and says it folds into a cube.
Why it is wrong
Four squares wrap around the cube, but squares five and six land on top of squares one and two, so two faces overlap while the top and bottom stay open. A correct cube net needs a cross or an L-shaped arrangement, with squares branching off the central strip.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Geometry and Measurement