How Many Edges And Vertices? Worksheet - Free Printable

I'll solve this worksheet by identifying each 3D shape and counting its faces, edges, and vertices.

Let me work through each shape systematically:

Shape 1: This is a triangular pyramid (also called a tetrahedron)
- Faces: 4 (1 base + 3 triangular sides)
- Edges: 6 (3 on the base + 3 connecting to the apex)
- Vertices: 4 (3 on the base + 1 at the top)

Shape 2: This is a cube
- Faces: 6 (all squares)
- Edges: 12 (4 on top + 4 on bottom + 4 vertical)
- Vertices: 8 (4 on top + 4 on bottom)

Shape 3: This is a pentagonal pyramid
- Faces: 6 (1 pentagon base + 5 triangular sides)
- Edges: 10 (5 on the base + 5 connecting to the apex)
- Vertices: 6 (5 on the base + 1 at the top)

Shape 4: This is a square pyramid
- Faces: 5 (1 square base + 4 triangular sides)
- Edges: 8 (4 on the base + 4 connecting to the apex)
- Vertices: 5 (4 on the base + 1 at the top)

Shape 5: This is a rectangular prism (cuboid)
- Faces: 6 (all rectangles)
- Edges: 12 (4 on top + 4 on bottom + 4 vertical)
- Vertices: 8 (4 on top + 4 on bottom)

Shape 6: This is a hexagonal prism
- Faces: 8 (2 hexagons on top/bottom + 6 rectangular sides)
- Edges: 18 (6 on top + 6 on bottom + 6 vertical)
- Vertices: 12 (6 on top + 6 on bottom)

Shape 7: This is a triangular prism
- Faces: 5 (2 triangles on ends + 3 rectangular sides)
- Edges: 9 (3 on one end + 3 on other end + 3 connecting them)
- Vertices: 6 (3 on one end + 3 on other end)

Shape 8: This is a hexagonal pyramid
- Faces: 7 (1 hexagon base + 6 triangular sides)
- Edges: 12 (6 on the base + 6 connecting to the apex)
- Vertices: 7 (6 on the base + 1 at the top)

Let me verify my counts using Euler's formula for polyhedra: V - E + F = 2

1) Triangular pyramid: 4 - 6 + 4 = 2 ✓
2) Cube: 8 - 12 + 6 = 2 ✓
3) Pentagonal pyramid: 6 - 10 + 6 = 2 ✓
4) Square pyramid: 5 - 8 + 5 = 2 ✓
5) Rectangular prism: 8 - 12 + 6 = 2 ✓
6) Hexagonal prism: 12 - 18 + 8 = 2 ✓
7) Triangular prism: 6 - 9 + 5 = 2 ✓
8) Hexagonal pyramid: 7 - 12 + 7 = 2 ✓

All calculations check out!

Final Answer:

1) Name: Triangular Pyramid (Tetrahedron)
Faces: 4, Edges: 6, Vertices: 4

2) Name: Cube
Faces: 6, Edges: 12, Vertices: 8

3) Name: Pentagonal Pyramid
Faces: 6, Edges: 10, Vertices: 6

4) Name: Square Pyramid
Faces: 5, Edges: 8, Vertices: 5

5) Name: Rectangular Prism (Cuboid)
Faces: 6, Edges: 12, Vertices: 8

6) Name: Hexagonal Prism
Faces: 8, Edges: 18, Vertices: 12

7) Name: Triangular Prism
Faces: 5, Edges: 9, Vertices: 6

8) Name: Hexagonal Pyramid
Faces: 7, Edges: 12, Vertices: 7