3D shapes & nets
The properties of 3D shapes
Every 3D shape can be described by its faces (flat surfaces), edges (where faces meet) and vertices (corners). Knowing these helps us name and compare shapes.
Faces, edges and vertices
• Face — a flat surface of a 3D shape. • Edge — the straight line where two faces meet. • Vertex — a corner where edges meet (more than one are called vertices).
Naming prisms
A prism has the same shape at each end and rectangles around the sides. A triangular prism has 2 triangles and 3 rectangles. A cuboid is a rectangular prism with 6 rectangular faces. A pentagonal prism has 2 pentagons and 5 rectangles.
Naming pyramids
A pyramid has one base and triangular faces that meet at a point (the apex). A square-based pyramid has 1 square and 4 triangles. A triangular-based pyramid (tetrahedron) has 4 triangular faces.
Curved shapes
Some shapes have curved surfaces. A cone has 1 flat circle face and 1 curved surface. A cylinder has 2 flat circle faces and 1 curved surface. A sphere has just 1 curved surface.
Worked examples
Faces of a square-based pyramid
- Count the flat surfaces.
- There is 1 square base and 4 triangular sides.
Answer: A square-based pyramid has 4 triangular faces and 1 square face, so 5 faces in total.
Edges and vertices of a cuboid
- Count the straight lines where faces meet, then count the corners.
- A cuboid has 12 edges and 8 vertices.
Answer: A cuboid has 6 faces, 12 edges and 8 vertices.
Naming a prism
- A shape has 2 triangular faces and 3 rectangular faces.
- The same shape at both ends with rectangles around the sides is a prism.
Answer: It is a triangular prism.
A curved shape
- A shape has 2 flat circle faces and 1 curved surface.
- Two circular ends joined by a curved surface is a cylinder.
Answer: It is a cylinder.
Where you see this in real life
- A dice is a cube with 6 square faces.
- A cereal box is a cuboid with 6 rectangular faces.
- A tin of beans is a cylinder; an ice-cream cone is a cone.
- Packaging designers and architects use 3D shapes to plan boxes and buildings.
Key words
- Face
- A flat surface of a 3D shape.
- Edge
- The straight line where two faces meet.
- Vertex
- A corner where edges meet (plural: vertices).
- Prism
- A 3D shape with the same shape at both ends and rectangles around the sides.
- Pyramid
- A 3D shape with a base and triangular faces meeting at a point.