Worksheet for identifying and analyzing the properties of 3D shapes.

I'll work through this problem step by step to find the properties of each 3D shape.

Let me analyze each shape:

1. Cube (already filled in as example)
- Faces: 6 ✓
- Edges: 12 ✓
- Vertices: 8 ✓
- Right angles on faces: 24 ✓

2. Triangular Prism
- Faces: A triangular prism has 2 triangular faces (top and bottom) + 3 rectangular faces (sides) = 5 faces
- Edges: Each triangle has 3 edges, so 2 triangles = 6 edges. Plus 3 vertical edges connecting them = 9 edges
- Vertices: Each triangle has 3 vertices, so 2 triangles = 6 vertices
- Right angles on faces: The 3 rectangular side faces each have 4 right angles = 3 × 4 = 12 right angles. The triangular faces don't have right angles (unless it's a right triangle, but we assume regular). So total = 12 right angles

3. Rectangular Prism (Cuboid)
- Faces: Top, bottom, front, back, left, right = 6 faces
- Edges: 4 edges on top + 4 edges on bottom + 4 vertical edges = 12 edges
- Vertices: 4 corners on top + 4 corners on bottom = 8 vertices
- Right angles on faces: All 6 faces are rectangles, each with 4 right angles = 6 × 4 = 24 right angles

4. Cylinder
- Faces: 2 circular faces (top and bottom) + 1 curved surface = 3 faces (or sometimes counted as 2 if curved surface isn't counted separately)
- Edges: 2 circular edges where the circles meet the curved surface = 2 edges
- Vertices: 0 vertices (no corners)
- Right angles on faces: 0 right angles (circles and curved surfaces have no right angles)

5. Square-based Pyramid
- Faces: 1 square base + 4 triangular sides = 5 faces
- Edges: 4 edges on the square base + 4 edges from base to apex = 8 edges
- Vertices: 4 corners on the base + 1 apex = 5 vertices
- Right angles on faces: The square base has 4 right angles. The triangular faces typically don't have right angles (unless specified). So = 4 right angles

Let me verify my calculations:

Triangular Prism: 5 faces, 9 edges, 6 vertices, 12 right angles ✓
Rectangular Prism: 6 faces, 12 edges, 8 vertices, 24 right angles ✓
Cylinder: 3 faces, 2 edges, 0 vertices, 0 right angles ✓
Square-based Pyramid: 5 faces, 8 edges, 5 vertices, 4 right angles ✓

Final Answer:

| Shape | Picture | Number of faces | Number of edges | Number of vertices | Number of right angles on faces |
|-------|---------|-----------------|-----------------|-------------------|--------------------------------|
| Cube | □ | 6 | 12 | 8 | 24 |
| Triangular prism | △▭ | 5 | 9 | 6 | 12 |
| Rectangular prism | | 6 | 12 | 8 | 24 |
| Cylinder | ⬭ | 3 | 2 | 0 | 0 |
| Square-based pyramid | ◇△ | 5 | 8 | 5 | 4 |