2nd Grade Math worksheet on identifying faces, edges, and vertices of 3D shapes.

Let's solve this step by step. We need to count the faces, edges, and vertices for each 3D shape shown in the worksheet.

---

Definitions:

- Face: A flat surface of a 3D shape.
- Edge: A line segment where two faces meet.
- Vertex (plural: vertices): A corner point where edges meet.

---

We'll go through each shape:

---

1) Triangular Prism

This is a prism with two triangular bases and three rectangular sides.

- Faces: 2 triangles + 3 rectangles = 5 faces
- Edges: Each triangle has 3 edges, but shared edges are counted once. Total: 9 edges
- 3 edges on top triangle, 3 on bottom, and 3 vertical edges connecting them → 9 edges
- Vertices: 3 vertices on top triangle, 3 on bottom → 6 vertices

✔ Faces: 5, Edges: 9, Vertices: 6

---

2) Cube

A cube has 6 square faces.

- Faces: 6 (top, bottom, front, back, left, right)
- Edges: Each face has 4 edges, but each edge is shared by 2 faces → 6 × 4 ÷ 2 = 12 edges
- Vertices: 8 corners

✔ Faces: 6, Edges: 12, Vertices: 8

---

3) Square Pyramid

A pyramid with a square base and 4 triangular faces meeting at a single apex.

- Faces: 1 square base + 4 triangles = 5 faces
- Edges: 4 edges on the base, and 4 edges from base to apex → 8 edges
- Vertices: 4 base vertices + 1 apex = 5 vertices

✔ Faces: 5, Edges: 8, Vertices: 5

---

4) Hexagonal Prism

A prism with two hexagonal bases and 6 rectangular sides.

- Faces: 2 hexagons + 6 rectangles = 8 faces
- Edges: Each hexagon has 6 edges → 6 × 2 = 12; plus 6 vertical edges connecting the bases → total 18 edges
- Vertices: 6 vertices per base → 6 × 2 = 12 vertices

✔ Faces: 8, Edges: 18, Vertices: 12

---

5) Rectangular Prism (Cuboid)

Same as a cube, but with rectangular faces.

- Faces: 6 (all rectangles)
- Edges: 12 (same as cube)
- Vertices: 8

✔ Faces: 6, Edges: 12, Vertices: 8

---

6) Octahedron (Regular Octahedron)

This is a Platonic solid with 8 triangular faces.

It looks like two square pyramids glued together at their bases.

- Faces: 8 equilateral triangles → 8 faces
- Edges: Each triangle has 3 edges, but shared → 8 × 3 ÷ 2 = 12 edges
- Vertices: 6 vertices (4 around the "equator", 1 top, 1 bottom)

✔ Faces: 8, Edges: 12, Vertices: 6

---

7) Pentagonal Pyramid

A pyramid with a pentagon base and 5 triangular faces.

- Faces: 1 pentagon base + 5 triangles = 6 faces
- Edges: 5 edges on base, 5 edges from base to apex → 10 edges
- Vertices: 5 base vertices + 1 apex = 6 vertices

✔ Faces: 6, Edges: 10, Vertices: 6

---

✔ Final Answers Table:

| Shape | Faces | Edges | Vertices |
|------|-------|--------|----------|
| 1) Triangular Prism | 5 | 9 | 6 |
| 2) Cube | 6 | 12 | 8 |
| 3) Square Pyramid | 5 | 8 | 5 |
| 4) Hexagonal Prism | 8 | 18 | 12 |
| 5) Rectangular Prism | 6 | 12 | 8 |
| 6) Octahedron | 8 | 12 | 6 |
| 7) Pentagonal Pyramid | 6 | 10 | 6 |

---

You can now fill these values into the table on the worksheet.

Let me know if you'd like a visual explanation or help understanding any shape!