Year 6: 3-D shapes and nets
Part of the Year 6 angles, shapes and circles chapter. Chapter overview · whole chapter on one page
3-D shapes and nets
A 3-D shape is a solid. Its flat sides are called faces. Two faces meet at an edge, and edges meet at a vertex.
A prism has two identical ends, and the same shape all the way along. A triangular prism has two triangular faces and three rectangular faces. A pyramid has a base, and triangular faces that all meet at one point called the apex.
| Shape | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Triangular prism | 5 | 9 | 6 |
| Square-based pyramid | 5 | 8 | 5 |
A net is a flat pattern that folds up into a 3-D shape. Each square of the net becomes one face, so a cube needs six squares. A net of a cube cannot have four squares that form a 2 by 2 block, because four faces cannot meet at one corner of a cube.
Key ideas
- A face is a flat side. An edge is where two faces meet. A vertex is a corner.
- A cube has 6 faces, 12 edges and 8 vertices.
- A net folds up to make a 3-D shape.
- A net of a cube has six squares, and each square covers a different face.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Count the faces, then the edges, then the vertices, one shape part at a time.
- Count the faces. Two triangles and three rectangles.2 + 3 = 5 faces
- Count the edges. The two triangles have 3 edges each, and the three rectangles share the other 3 edges.3 + 3 + 3 = 9 edges
- Count the vertices. Each triangle has 3 corners, and the two triangles give 6 corners in total.3 + 3 = 6 vertices
Check. Check: faces + vertices = edges + 2 for a prism, so 5 + 6 = 9 + 2. ✓
Watch out. A triangular prism has 5 faces, 9 edges and 6 vertices. Do not count a hidden edge twice.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Check that the net has six squares, and that it has no 2 by 2 block.
- Count the squares. A cube has 6 faces, so the net needs 6 squares.6 squares
- Look for a 2 by 2 block. Four squares in a block would all meet at one corner, which cannot happen on a cube.no 2 by 2 block
- Check the shape. The row of four wraps round the sides. One square goes on top and one goes underneath.row of 4, 1 above, 1 below
- Write the answer. This net folds up into a cube.Yes
Check. Each of the six squares folds onto a different face. ✓
Watch out. The cross shape with a row of four is a cube net. Count the squares first.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Find the area of one square face, then multiply by the six faces of the net.
- Find the area of one square. Area of a square = side × side.3 × 3 = 9 cm²
- Count the squares in the net. A cube has 6 faces, so the net has 6 squares.6 squares
- Multiply the area of one square by 6. Each square is the same size, so the total area is 6 lots of 9.6 × 9 = 54
- Write the answer. The total area of the net is in square centimetres.54
Check. 54 ÷ 6 = 9, which is the area of one face. ✓
Watch out. Find the area of one face first. Do not use the length of the edge as the area.
Exercise 10F Practice: faces, edges, vertices and nets
Non-calculatorKey words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Count the flat faces of the prism.
- Count the triangles. There are two triangular ends.2 triangles
- Count the rectangles. The three sides between the ends are rectangles.3 rectangles
- Write the answer. Add the two kinds of face.2 + 3 = 5
Check. A prism with a triangular end has 3 + 2 = 5 faces. ✓
Watch out. Do not forget the two ends.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Each end has 3 edges, and the three sides join the ends.
- Count the edges on one end. A triangle has 3 edges.3 edges
- Count the edges on the other end. The other end also has 3 edges.3 + 3 = 6
- Add the edges that join the ends. There are 3 of these, one at each corner.6 + 3 = 9
Check. Each of the 6 vertices has 3 edges, so the edges are 6 × 3 ÷ 2 = 9. ✓
Watch out. The edges that join the two ends are easy to miss. There are three of them.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. A vertex is a corner. Count the corners on each end.
- Count the corners on one end. A triangle has 3 corners.3 vertices
- Count the corners on both ends. The other end has 3 more.3 + 3 = 6
Check. Each end has 3 corners, and 3 + 3 = 6. ✓
Watch out. A vertex is a corner. Do not count the edges.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Look at the faces that meet at the top point.
- Find the triangles. Each side of the square base has one triangle that meets the top point.4 sides = 4 triangles
- Write the answer. The base is a square, not a triangle, so it is not counted.4
Check. A square-based pyramid has 4 triangular faces and 1 square base, 5 faces altogether. ✓
Watch out. The base is a square, so it is not a triangular face.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Count the edges: 4 around the base and 4 going up to the top point.
- Count the edges around the base. A square base has 4 edges.4 edges
- Count the edges up to the top point. Four edges join the four corners of the base to the apex.4 edges
- Add them up. This gives the number of edges.4 + 4 = 8
Check. A square-based pyramid has 8 edges. ✓
Watch out. Count the sloping edges as well as the base edges.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. A vertex is a corner. Count the corners of the base and the apex.
- Count the corners of the base. A square has 4 corners.4 corners
- Add the apex. The top point is also a corner.4 + 1 = 5
Check. A square-based pyramid has 5 vertices, which is 4 + 1. ✓
Watch out. The top point counts as a vertex.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Fold the net in your mind. Each square becomes one face of the cube.
- Count the squares. The net has a row of four squares, one above and one below.4 + 1 + 1 = 6 squares
- Think about the shape the net makes. A row of four wraps round four sides, and the two single squares make the top and bottom.four sides, top and bottom
- Write the answer. The shape is a cube, because all six faces are squares.cube
Check. A cube has 6 square faces, so this net folds into a cube. ✓
Watch out. Look at the number of squares and their shape to name the 3-D shape.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Use the rule for cube nets: six squares, and no 2 by 2 block of squares.
- Check net A. Two squares sit on the same side of the row, so two faces fold onto the same face of the cube. One face is missing.A: not a cube
- Check net B. Squares in a 2 by 2 block would meet at one corner, which cannot happen on a cube.B: 2 by 2 block
- Check net C. The row of four wraps round the sides, with one square above and one below, at different places. Each square folds onto a different face.C: folds into a cube
- Check net D. Net D has a 2 by 3 block of squares, so it cannot fold into a cube.D: 2 by 3 block
- Write the answer. Only net C folds into a cube.C
Check. The nets are checked by rolling a cube over each one: only C gives six different faces. ✓
Watch out. Check each square of the net against the cube. A correct net has no 2 by 2 block and no two squares on the same face.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Find the area of one square face, then multiply by the six faces of the cube net.
- Find the area of one square. Area of a square = side × side.3 × 3 = 9 cm²
- Multiply by the six squares. The net has six squares, one for each face.6 × 9 = 54
- Write the answer. The total area is in square centimetres.54
Check. 54 ÷ 9 = 6 squares. ✓
Watch out. Area is in square units, so write cm².
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Multiply the three lengths of the cuboid.
- Find the number of cubes along the length, width and height. The cuboid is 4 cubes long, 3 cubes wide and 2 cubes high.4, 3 and 2
- Multiply the three numbers. Each cube fits into one place in the layers.4 × 3 × 2 = 24
- Write the answer. It takes 24 cubes to build the cuboid.24
Check. Two layers of 4 × 3 = 12 cubes each, so 12 + 12 = 24. ✓
Watch out. Multiply the three lengths. Do not add them.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Subtract the vertices of the pyramid from the vertices of the cube.
- Find the vertices of the cube. A cube has 8 corners.8 vertices
- Find the vertices of the pyramid. A square-based pyramid has 5 corners.5 vertices
- Find the difference. The cube has this many more.8 - 5 = 3
Check. 5 + 3 = 8. ✓
Watch out. Subtract the smaller number from the bigger one.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Follow the squares round the cube, one face at a time.
- Fold the row of six. Four squares wrap round the sides of a cube, so the fifth square lands on the first side again.fifth square = first face
- Check the faces. Two squares cover the same face, so there are not six different faces.faces repeat
- Write the answer. Sam is not right. A row of six squares does not fold into a cube.No
Check. A row of four squares wraps round the cube, so a row of six must overlap itself. ✓
Watch out. A net of a cube is never a single row of six squares.
Key words. A face is a flat side. An edge is where two faces meet. A vertex (plural vertices) is a corner. A net is a flat pattern that folds up to make a 3-D shape.
Method. Think about the corners of a cube and how many faces meet at each one.
- Look at a corner of a cube. Three faces meet at each corner of a cube.3 faces at each corner
- Look at the four squares in a 2 by 2 block. In a block of four squares, all four would meet at the same point.4 squares at one point
- Write the answer. Four squares cannot all meet at one corner of a cube, so the block cannot fold up.4 > 3, so it cannot fold
Check. A cube has no corner where four faces meet, so a 2 by 2 block can never be part of a cube net. ✓
Watch out. Think about the corners of the cube, not the faces in the middle.
Watch out
Common mistake: counting the faces of a prism without the two ends, or counting edges and vertices as if they were faces. Also, a net must have one square for each face: a row of six does not fold into a cube.
Exam tip
To check a net, count the squares first. Then look for any block of four squares, because a cube has no 2 by 2 block in its net.