2D and 3D Shapes Worksheets | FREEBIE! | Made By Teachers - Free Printable

Let's solve this step-by-step. The task is to identify the name, vertices, faces, and edges for each 3D shape shown, and then use the given properties in the extension section to determine the names of shapes A, B, and C.

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🔷 Definitions:

- Vertices: Corners (points where edges meet).
- Faces: Flat surfaces (including curved ones if applicable).
- Edges: Lines where two faces meet.
- Prism: A solid with two identical ends and flat sides. The cross-section is the same along its length.
- Pyramid: A solid with a base and triangular faces meeting at a common vertex.

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## ✔ Part 1: Identify Shapes 1–9

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1) Rectangular Prism (Cuboid)

- Name: Rectangular prism (or cuboid)
- Vertices: 8
- Faces: 6 (all rectangles)
- Edges: 12

✔ *This is a standard box-like shape.*

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2) Triangular Prism

- Name: Triangular prism
- Vertices: 6
- Faces: 5 (2 triangles + 3 rectangles)
- Edges: 9

✔ *Two triangular bases and three rectangular sides.*

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3) Cone

- Name: Cone
- Vertices: 1 (the tip)
- Faces: 2 (1 circular base + 1 curved surface)
- Edges: 1 (the circular edge of the base)

⚠️ Note: Technically, a cone has no edges in strict geometric terms because the curved surface doesn’t meet another face with a straight line. But many curricula count the base edge as an edge → so 1 edge is acceptable here.

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4) Tetrahedron (Triangular Pyramid)

- Name: Tetrahedron or triangular pyramid
- Vertices: 4
- Faces: 4 (all triangles)
- Edges: 6

✔ *All faces are triangles; it’s a pyramid with a triangular base.*

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5) Cylinder

- Name: Cylinder
- Vertices: 0 (no sharp corners)
- Faces: 3 (2 circular bases + 1 curved surface)
- Edges: 2 (the two circular edges)

⚠️ Again, some sources say cylinders have 0 edges (since no straight lines), but in basic math, we often consider the circular boundaries as edges → so 2 edges.

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6) Cube

- Name: Cube
- Vertices: 8
- Faces: 6 (all squares)
- Edges: 12

✔ *Special case of a rectangular prism where all sides are equal.*

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7) Sphere

- Name: Sphere
- Vertices: 0
- Faces: 1 (entirely curved surface)
- Edges: 0

✔ *No flat faces, no edges, no vertices.*

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8) Square Pyramid

- Name: Square pyramid
- Vertices: 5 (4 at base + 1 apex)
- Faces: 5 (1 square base + 4 triangles)
- Edges: 8

✔ *Base is a square, four triangular faces meet at the top.*

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9) Pentagonal Prism

- Name: Pentagonal prism
- Vertices: 10 (5 on each end)
- Faces: 7 (2 pentagons + 5 rectangles)
- Edges: 15

✔ *Two pentagonal bases connected by five rectangular sides.*

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## ✔ Extension: Identify Shapes A, B, C

We're told:
- A and B are prisms
- C is a pyramid

We’re given:
| Shape | Vertices | Faces | Edges |
|-------|----------|--------|--------|
| A | 12 | 8 | 18 |
| B | 16 | 10 | 24 |
| C | 6 | 6 | 10 |

Let’s analyze:

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🔹 Shape A: Prism with V=12, F=8, E=18

For prisms:
- Number of vertices = 2 × n (n = number of sides of base)
- Number of faces = n + 2 (n lateral faces + 2 bases)
- Number of edges = 3n

Let’s solve:
- V = 2n → 12 = 2n → n = 6
- So base is a hexagon
- Faces: n + 2 = 6 + 2 = 8 ✔
- Edges: 3n = 3×6 = 18 ✔

➡️ Shape A: Hexagonal prism

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🔹 Shape B: Prism with V=16, F=10, E=24

V = 2n → 16 = 2n → n = 8

So base is an octagon

Faces: n + 2 = 8 + 2 = 10 ✔
Edges: 3n = 3×8 = 24 ✔

➡️ Shape B: Octagonal prism

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🔹 Shape C: Pyramid with V=6, F=6, E=10

For pyramids:
- Vertices = n + 1 (n from base, 1 apex)
- Faces = n + 1 (n triangular faces + 1 base)
- Edges = 2n

Given:
- V = 6 → n + 1 = 6 → n = 5
- So base is a pentagon
- Faces: n + 1 = 5 + 1 = 6 ✔
- Edges: 2n = 2×5 = 10 ✔

➡️ Shape C: Pentagonal pyramid

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## ✔ Final Answers:

Part 1: Shapes 1–9

| # | Name | Vertices | Faces | Edges |
|---|--------------------|----------|--------|--------|
| 1 | Rectangular prism | 8 | 6 | 12 |
| 2 | Triangular prism | 6 | 5 | 9 |
| 3 | Cone | 1 | 2 | 1 |
| 4 | Tetrahedron | 4 | 4 | 6 |
| 5 | Cylinder | 0 | 3 | 2 |
| 6 | Cube | 8 | 6 | 12 |
| 7 | Sphere | 0 | 1 | 0 |
| 8 | Square pyramid | 5 | 5 | 8 |
| 9 | Pentagonal prism | 10 | 7 | 15 |

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🟨 Extension:

| Shape | Name |
|-------|-------------------|
| A | Hexagonal prism |
| B | Octagonal prism |
| C | Pentagonal pyramid|

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Let me know if you'd like this formatted as a printable answer sheet!