Math worksheet for kids to practice identifying and counting vertices, edges, and faces of 3D shapes.
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Step-by-step solution for: Pin on Math Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Pin on Math Worksheets
To solve the problem of counting the number of vertices, edges, and faces for each figure in the image, we will analyze each shape step by step. Here's the breakdown:
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- Vertices: A triangular pyramid has 4 vertices (one at the apex and three at the base).
- Edges: It has 6 edges (3 edges on the base triangle and 3 edges connecting the apex to each vertex of the base).
- Faces: It has 4 faces (1 triangular base and 3 triangular lateral faces).
Answer:
- Edges: 6
- Faces: 4
- Vertices: 4
---
- Vertices: A square pyramid has 5 vertices (4 at the base and 1 at the apex).
- Edges: It has 8 edges (4 edges on the square base and 4 edges connecting the apex to each vertex of the base).
- Faces: It has 5 faces (1 square base and 4 triangular lateral faces).
Answer:
- Edges: 8
- Faces: 5
- Vertices: 5
---
- Vertices: A hexagonal prism has 12 vertices (6 at the top hexagon and 6 at the bottom hexagon).
- Edges: It has 18 edges (6 edges on the top hexagon, 6 edges on the bottom hexagon, and 6 vertical edges connecting corresponding vertices of the two hexagons).
- Faces: It has 8 faces (2 hexagonal bases and 6 rectangular lateral faces).
Answer:
- Edges: 18
- Faces: 8
- Vertices: 12
---
- Vertices: A rectangular prism has 8 vertices (4 at the top rectangle and 4 at the bottom rectangle).
- Edges: It has 12 edges (4 edges on the top rectangle, 4 edges on the bottom rectangle, and 4 vertical edges connecting corresponding vertices of the two rectangles).
- Faces: It has 6 faces (2 rectangular bases and 4 rectangular lateral faces).
Answer:
- Edges: 12
- Faces: 6
- Vertices: 8
---
- Vertices: An octagonal prism has 16 vertices (8 at the top octagon and 8 at the bottom octagon).
- Edges: It has 24 edges (8 edges on the top octagon, 8 edges on the bottom octagon, and 8 vertical edges connecting corresponding vertices of the two octagons).
- Faces: It has 10 faces (2 octagonal bases and 8 rectangular lateral faces).
Answer:
- Edges: 24
- Faces: 10
- Vertices: 16
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- Vertices: A cylinder does not have any vertices because it has curved surfaces.
- Edges: A cylinder does not have any edges because its surfaces are curved.
- Faces: A cylinder has 3 faces (2 circular bases and 1 curved surface).
Answer:
- Edges: 0
- Faces: 3
- Vertices: 0
---
- Vertices: A triangular prism has 6 vertices (3 at the top triangle and 3 at the bottom triangle).
- Edges: It has 9 edges (3 edges on the top triangle, 3 edges on the bottom triangle, and 3 vertical edges connecting corresponding vertices of the two triangles).
- Faces: It has 5 faces (2 triangular bases and 3 rectangular lateral faces).
Answer:
- Edges: 9
- Faces: 5
- Vertices: 6
---
- Vertices: A cone has 1 vertex (the apex).
- Edges: A cone does not have any edges because its surfaces are curved.
- Faces: A cone has 2 faces (1 circular base and 1 curved surface).
Answer:
- Edges: 0
- Faces: 2
- Vertices: 1
---
1. a: Edges = 6, Faces = 4, Vertices = 4
2. b: Edges = 8, Faces = 5, Vertices = 5
3. c: Edges = 18, Faces = 8, Vertices = 12
4. d: Edges = 12, Faces = 6, Vertices = 8
5. e: Edges = 24, Faces = 10, Vertices = 16
6. f: Edges = 0, Faces = 3, Vertices = 0
7. g: Edges = 9, Faces = 5, Vertices = 6
8. h: Edges = 0, Faces = 2, Vertices = 1
---
\[
\boxed{
\begin{array}{ccc}
\text{a} & \text{b} & \text{c} \\
\text{Edges: 6} & \text{Edges: 8} & \text{Edges: 18} \\
\text{Faces: 4} & \text{Faces: 5} & \text{Faces: 8} \\
\text{Vertices: 4} & \text{Vertices: 5} & \text{Vertices: 12} \\
\hline
\text{d} & \text{e} & \text{f} \\
\text{Edges: 12} & \text{Edges: 24} & \text{Edges: 0} \\
\text{Faces: 6} & \text{Faces: 10} & \text{Faces: 3} \\
\text{Vertices: 8} & \text{Vertices: 16} & \text{Vertices: 0} \\
\hline
\text{g} & \text{h} & \\
\text{Edges: 9} & \text{Edges: 0} & \\
\text{Faces: 5} & \text{Faces: 2} & \\
\text{Vertices: 6} & \text{Vertices: 1} & \\
\end{array}
}
\]
---
Figure a: Triangular Pyramid
- Vertices: A triangular pyramid has 4 vertices (one at the apex and three at the base).
- Edges: It has 6 edges (3 edges on the base triangle and 3 edges connecting the apex to each vertex of the base).
- Faces: It has 4 faces (1 triangular base and 3 triangular lateral faces).
Answer:
- Edges: 6
- Faces: 4
- Vertices: 4
---
Figure b: Square Pyramid
- Vertices: A square pyramid has 5 vertices (4 at the base and 1 at the apex).
- Edges: It has 8 edges (4 edges on the square base and 4 edges connecting the apex to each vertex of the base).
- Faces: It has 5 faces (1 square base and 4 triangular lateral faces).
Answer:
- Edges: 8
- Faces: 5
- Vertices: 5
---
Figure c: Hexagonal Prism
- Vertices: A hexagonal prism has 12 vertices (6 at the top hexagon and 6 at the bottom hexagon).
- Edges: It has 18 edges (6 edges on the top hexagon, 6 edges on the bottom hexagon, and 6 vertical edges connecting corresponding vertices of the two hexagons).
- Faces: It has 8 faces (2 hexagonal bases and 6 rectangular lateral faces).
Answer:
- Edges: 18
- Faces: 8
- Vertices: 12
---
Figure d: Rectangular Prism
- Vertices: A rectangular prism has 8 vertices (4 at the top rectangle and 4 at the bottom rectangle).
- Edges: It has 12 edges (4 edges on the top rectangle, 4 edges on the bottom rectangle, and 4 vertical edges connecting corresponding vertices of the two rectangles).
- Faces: It has 6 faces (2 rectangular bases and 4 rectangular lateral faces).
Answer:
- Edges: 12
- Faces: 6
- Vertices: 8
---
Figure e: Octagonal Prism
- Vertices: An octagonal prism has 16 vertices (8 at the top octagon and 8 at the bottom octagon).
- Edges: It has 24 edges (8 edges on the top octagon, 8 edges on the bottom octagon, and 8 vertical edges connecting corresponding vertices of the two octagons).
- Faces: It has 10 faces (2 octagonal bases and 8 rectangular lateral faces).
Answer:
- Edges: 24
- Faces: 10
- Vertices: 16
---
Figure f: Cylinder
- Vertices: A cylinder does not have any vertices because it has curved surfaces.
- Edges: A cylinder does not have any edges because its surfaces are curved.
- Faces: A cylinder has 3 faces (2 circular bases and 1 curved surface).
Answer:
- Edges: 0
- Faces: 3
- Vertices: 0
---
Figure g: Triangular Prism
- Vertices: A triangular prism has 6 vertices (3 at the top triangle and 3 at the bottom triangle).
- Edges: It has 9 edges (3 edges on the top triangle, 3 edges on the bottom triangle, and 3 vertical edges connecting corresponding vertices of the two triangles).
- Faces: It has 5 faces (2 triangular bases and 3 rectangular lateral faces).
Answer:
- Edges: 9
- Faces: 5
- Vertices: 6
---
Figure h: Cone
- Vertices: A cone has 1 vertex (the apex).
- Edges: A cone does not have any edges because its surfaces are curved.
- Faces: A cone has 2 faces (1 circular base and 1 curved surface).
Answer:
- Edges: 0
- Faces: 2
- Vertices: 1
---
Final Answers
1. a: Edges = 6, Faces = 4, Vertices = 4
2. b: Edges = 8, Faces = 5, Vertices = 5
3. c: Edges = 18, Faces = 8, Vertices = 12
4. d: Edges = 12, Faces = 6, Vertices = 8
5. e: Edges = 24, Faces = 10, Vertices = 16
6. f: Edges = 0, Faces = 3, Vertices = 0
7. g: Edges = 9, Faces = 5, Vertices = 6
8. h: Edges = 0, Faces = 2, Vertices = 1
---
Boxed Final Answer
\[
\boxed{
\begin{array}{ccc}
\text{a} & \text{b} & \text{c} \\
\text{Edges: 6} & \text{Edges: 8} & \text{Edges: 18} \\
\text{Faces: 4} & \text{Faces: 5} & \text{Faces: 8} \\
\text{Vertices: 4} & \text{Vertices: 5} & \text{Vertices: 12} \\
\hline
\text{d} & \text{e} & \text{f} \\
\text{Edges: 12} & \text{Edges: 24} & \text{Edges: 0} \\
\text{Faces: 6} & \text{Faces: 10} & \text{Faces: 3} \\
\text{Vertices: 8} & \text{Vertices: 16} & \text{Vertices: 0} \\
\hline
\text{g} & \text{h} & \\
\text{Edges: 9} & \text{Edges: 0} & \\
\text{Faces: 5} & \text{Faces: 2} & \\
\text{Vertices: 6} & \text{Vertices: 1} & \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of 3d shapes faces edges vertices worksheets with answers.
