3D Shapes Worksheet for Learning Geometry

The image shows a worksheet focused on identifying properties of 3D shapes, specifically the number of edges, faces/surfaces, and vertices for common 3D shapes. The worksheet includes diagrams of:

1. Square-based pyramid
2. Cube
3. Cuboid (rectangular prism)
4. Triangular prism
5. Cylinder
6. Triangular-based pyramid (tetrahedron)

We’ll solve this step by step for each shape.

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🔷 1. Square-based Pyramid

- Shape: A pyramid with a square base and four triangular faces meeting at a point (apex).
- Edges:
- 4 edges on the square base
- 4 edges from each corner of the base to the apex
→ Total: 8 edges
- Faces/Surfaces:
- 1 square base
- 4 triangular sides
→ Total: 5 faces
- Vertices:
- 4 corners on the base
- 1 apex
→ Total: 5 vertices

✔ Answer:
- Edges: 8
- Faces: 5
- Vertices: 5

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🔷 2. Cube

- Shape: All six faces are squares.
- Edges:
- Each face has 4 edges, but each edge is shared by two faces
→ Total: 12 edges
- Faces/Surfaces:
- 6 square faces
→ Total: 6 faces
- Vertices:
- 8 corners
→ Total: 8 vertices

✔ Answer:
- Edges: 12
- Faces: 6
- Vertices: 8

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🔷 3. Cuboid (Rectangular Prism)

- Shape: Like a cube but with rectangular faces (not necessarily all equal).
- Edges:
- Same as a cube: 12 edges
→ Total: 12 edges
- Faces/Surfaces:
- 6 rectangular faces (opposite faces are equal)
→ Total: 6 faces
- Vertices:
- 8 corners
→ Total: 8 vertices

✔ Answer:
- Edges: 12
- Faces: 6
- Vertices: 8

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🔷 4. Triangular Prism

- Shape: Two triangular bases connected by three rectangular faces.
- Edges:
- 3 edges on each triangle (top and bottom) → 3 × 2 = 6
- 3 vertical edges connecting the triangles
→ Total: 9 edges
- Faces/Surfaces:
- 2 triangular bases
- 3 rectangular lateral faces
→ Total: 5 faces
- Vertices:
- 3 vertices per triangle → 3 × 2 = 6 vertices

✔ Answer:
- Edges: 9
- Faces: 5
- Vertices: 6

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🔷 5. Cylinder

- Shape: Two circular bases connected by a curved surface.
- Edges:
- Cylinders have no straight edges (they are curved).
- However, some curricula count the circular boundaries as "edges" (though technically not edges in geometry).
→ In elementary math, often considered to have 0 edges (since no sharp edges), or sometimes 2 (the top and bottom rims).
But strictly speaking, cylinders have:
- No edges (in polyhedra terms)
- 2 circular faces
- No vertices
- Faces/Surfaces:
- 2 flat circular faces
- 1 curved surface
→ Total: 3 surfaces (but only 2 are flat faces)
- Vertices:
- No corners → 0 vertices

✔ Answer (commonly accepted in primary education):
- Edges: 0 (or sometimes 2 — depends on curriculum)
- Faces: 2 (if only counting flat ones) or 3 (including curved surface)
- Vertices: 0

But since this is likely for younger students, it's usually taught as:
- Edges: 0
- Faces: 3 (2 circles + 1 curved surface)
- Vertices: 0

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🔷 6. Triangular-based Pyramid (Tetrahedron)

- Shape: A pyramid with a triangular base and three triangular faces.
- Edges:
- 3 edges on the base
- 3 edges from base corners to apex
→ Total: 6 edges
- Faces/Surfaces:
- 4 triangular faces (base + 3 sides)
→ Total: 4 faces
- Vertices:
- 3 on the base + 1 apex
→ Total: 4 vertices

✔ Answer:
- Edges: 6
- Faces: 4
- Vertices: 4

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✔ Final Answers Summary:

| Shape | Edges | Faces | Vertices |
|------|-------|--------|----------|
| Square-based Pyramid | 8 | 5 | 5 |
| Cube | 12 | 6 | 8 |
| Cuboid | 12 | 6 | 8 |
| Triangular Prism | 9 | 5 | 6 |
| Cylinder | 0 | 3 | 0 |
| Triangular-based Pyramid | 6 | 4 | 4 |

> 🟩 Note: For cylinder, answers may vary slightly depending on whether curved surfaces are counted as "faces" and if circular rims are called "edges". This version uses standard elementary math conventions.

Let me know if you'd like this formatted as a completed worksheet!