Numeracy: Properties of 3D shapes | Worksheet | PrimaryLeap.co.uk - Free Printable

To solve the problem, we need to fill in the missing properties (Edges, Faces, Vertices) for each 3D shape listed in the table. Let's go through each shape step by step:

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1. Hexagonal Prism

- Shape: A hexagonal prism has two hexagonal bases and six rectangular lateral faces.
- Edges: There are 6 edges on the top hexagon, 6 edges on the bottom hexagon, and 6 vertical edges connecting corresponding vertices of the two hexagons.
Total: \(6 + 6 + 6 = 18\)
- Faces: There are 2 hexagonal faces (top and bottom) and 6 rectangular faces.
Total: \(2 + 6 = 8\)
- Vertices: There are 6 vertices on the top hexagon and 6 vertices on the bottom hexagon.
Total: \(6 + 6 = 12\)

Summary for Hexagonal Prism:
- Edges: 18
- Faces: 8
- Vertices: 12

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2. Octahedron

- Shape: An octahedron is a polyhedron with 8 equilateral triangular faces.
- Edges: Each edge is shared by 2 triangular faces. Since there are 8 faces and each face has 3 edges, the total number of edges is calculated as:
\[
\text{Edges} = \frac{8 \times 3}{2} = 12
\]
- Faces: By definition, an octahedron has 8 faces.
- Vertices: Each vertex is shared by 4 triangular faces. Since there are 8 faces and each face has 3 vertices, the total number of vertices is calculated as:
\[
\text{Vertices} = \frac{8 \times 3}{3} = 6
\]

Summary for Octahedron:
- Edges: 12
- Faces: 8
- Vertices: 6

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3. Triangular Prism

- Shape: A triangular prism has two triangular bases and three rectangular lateral faces.
- Edges: There are 3 edges on the top triangle, 3 edges on the bottom triangle, and 3 vertical edges connecting corresponding vertices of the two triangles.
Total: \(3 + 3 + 3 = 9\)
- Faces: There are 2 triangular faces (top and bottom) and 3 rectangular faces.
Total: \(2 + 3 = 5\)
- Vertices: There are 3 vertices on the top triangle and 3 vertices on the bottom triangle.
Total: \(3 + 3 = 6\)

Summary for Triangular Prism:
- Edges: 9
- Faces: 5
- Vertices: 6

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4. Cylinder

- Shape: A cylinder has two circular bases and one curved surface.
- Edges: A cylinder does not have any edges because its surfaces are smooth and continuous.
- Faces: A cylinder has 2 flat circular faces (top and bottom) and 1 curved surface, but the curved surface is not considered a "face" in the traditional sense of polyhedra. Therefore, it has only 2 faces.
- Vertices: A cylinder does not have any vertices because it has no sharp corners.

Summary for Cylinder:
- Edges: 0
- Faces: 2
- Vertices: 0

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5. Hexagonal Pyramid

- Shape: A hexagonal pyramid has a hexagonal base and 6 triangular faces that meet at a single apex.
- Edges: There are 6 edges on the hexagonal base and 6 edges connecting each vertex of the base to the apex.
Total: \(6 + 6 = 12\)
- Faces: There is 1 hexagonal face (the base) and 6 triangular faces.
Total: \(1 + 6 = 7\)
- Vertices: There are 6 vertices on the hexagonal base and 1 apex.
Total: \(6 + 1 = 7\)

Summary for Hexagonal Pyramid:
- Edges: 12
- Faces: 7
- Vertices: 7

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6. Square Pyramid

- Shape: A square pyramid has a square base and 4 triangular faces that meet at a single apex.
- Edges: There are 4 edges on the square base and 4 edges connecting each vertex of the base to the apex.
Total: \(4 + 4 = 8\)
- Faces: There is 1 square face (the base) and 4 triangular faces.
Total: \(1 + 4 = 5\)
- Vertices: There are 4 vertices on the square base and 1 apex.
Total: \(4 + 1 = 5\)

Summary for Square Pyramid:
- Edges: 8
- Faces: 5
- Vertices: 5

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7. Cone

- Shape: A cone has a circular base and a curved surface that tapers to a single vertex (apex).
- Edges: A cone does not have any edges because its surfaces are smooth and continuous.
- Faces: A cone has 1 flat circular face (the base) and 1 curved surface, but the curved surface is not considered a "face" in the traditional sense of polyhedra. Therefore, it has only 1 face.
- Vertices: A cone has 1 vertex (the apex).

Summary for Cone:
- Edges: 0
- Faces: 1
- Vertices: 1

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8. Tetrahedron

- Shape: A tetrahedron is a polyhedron with 4 equilateral triangular faces.
- Edges: Each edge is shared by 2 triangular faces. Since there are 4 faces and each face has 3 edges, the total number of edges is calculated as:
\[
\text{Edges} = \frac{4 \times 3}{2} = 6
\]
- Faces: By definition, a tetrahedron has 4 faces.
- Vertices: Each vertex is shared by 3 triangular faces. Since there are 4 faces and each face has 3 vertices, the total number of vertices is calculated as:
\[
\text{Vertices} = \frac{4 \times 3}{3} = 4
\]

Summary for Tetrahedron:
- Edges: 6
- Faces: 4
- Vertices: 4

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Final Answer

Here is the completed table:

| Shape | Name | Edges | Faces | Vertices |
|------------------|------------------|-------|-------|----------|
| | Hexagonal prism | 18 | 8 | 12 |
| | Octahedron | 12 | 8 | 6 |
| | Triangular prism | 9 | 5 | 6 |
| | Cylinder | 0 | 2 | 0 |
| | Hexagonal pyramid| 12 | 7 | 7 |
| | Square pyramid | 8 | 5 | 5 |
| | Cone | 0 | 1 | 1 |
| | Tetrahedron | 6 | 4 | 4 |

Boxed Final Answer:
\[
\boxed{
\begin{array}{|c|c|c|c|c|}
\hline
\text{Shape} & \text{Name} & \text{Edges} & \text{Faces} & \text{Vertices} \\
\hline
& \text{Hexagonal prism} & 18 & 8 & 12 \\
\hline
& \text{Octahedron} & 12 & 8 & 6 \\
\hline
& \text{Triangular prism} & 9 & 5 & 6 \\
\hline
& \text{Cylinder} & 0 & 2 & 0 \\
\hline
& \text{Hexagonal pyramid} & 12 & 7 & 7 \\
\hline
& \text{Square pyramid} & 8 & 5 & 5 \\
\hline
& \text{Cone} & 0 & 1 & 1 \\
\hline
& \text{Tetrahedron} & 6 & 4 & 4 \\
\hline
\end{array}
}
\]