Overview of common polyhedra with their properties and visual representations.
Educational worksheet: 3d Shapes Worksheets. Download and print for classroom or home learning activities.
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Step-by-step solution for: 3d Shapes Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: 3d Shapes Worksheets
The image provided is an informational chart about four different polyhedra: the Cuboid, Triangular prism, Dodecahedron, and Square based pyramid. It lists their properties (Faces, Edges, Vertices) and shows a visual representation.
Since there is no specific question asked in the prompt or visible in the image (such as "How many edges does a dodecahedron have?" or "Which shape has 5 faces?"), I cannot provide a single numerical "Final Answer" to a specific problem.
However, based on the structure of the request, it appears the user may want me to verify the information presented or perhaps identify a discrepancy if one exists. Let's carefully check the mathematical accuracy of the data provided for each shape using Euler's Formula for polyhedra: $F + V - E = 2$ (where F=Faces, V=Vertices, E=Edges).
Step 1: Check the Cuboid
* Given: Faces = 6, Edges = 12, Vertices = 8.
* Check with Euler's Formula: $6 + 8 - 12 = 2$.
* $14 - 12 = 2$. This is correct.
* Description: "A cuboid can be described as a rectangular prism." This is correct.
Step 2: Check the Triangular Prism
* Given: Faces = 5, Edges = 9, Vertices = 6.
* Check with Euler's Formula: $5 + 6 - 9 = 2$.
* $11 - 9 = 2$. This is correct.
* Structure: A triangular prism has 2 triangular bases and 3 rectangular sides. Total faces = 5. Correct.
Step 3: Check the Dodecahedron
* Given: Faces = 12, Edges = 30, Vertices = 20.
* Check with Euler's Formula: $12 + 20 - 30 = 2$.
* $32 - 30 = 2$. This is correct.
* Description: "This shape is one of the five platonic solids." This is correct. A regular dodecahedron is indeed a Platonic solid.
Step 4: Check the Square Based Pyramid
* Given: Faces = 5, Edges = 8, Vertices = 5.
* Check with Euler's Formula: $5 + 5 - 8 = 2$.
* $10 - 8 = 2$. This is correct.
* Structure: A square base (1 face) + 4 triangular sides = 5 faces. Correct.
Conclusion:
All the data presented in the chart is mathematically accurate. There are no errors in the counts of faces, edges, or vertices for any of the shapes listed.
Since no specific question was asked, I will summarize the key data points from the chart as the "answer" to what is likely a study or reference task. If this was a "find the error" task, there are no errors. If it was a "read the table" task, the information is verified.
I will provide a summary of the verified properties as the final output, as this is the most helpful response when no specific question is posed but data validation is implied.
Final Answer:
The information in the chart is correct. Here are the verified properties for each polyhedron:
1. Cuboid: 6 Faces, 12 Edges, 8 Vertices.
2. Triangular Prism: 5 Faces, 9 Edges, 6 Vertices.
3. Dodecahedron: 12 Faces, 30 Edges, 20 Vertices.
4. Square Based Pyramid: 5 Faces, 8 Edges, 5 Vertices.
All shapes satisfy Euler's formula ($Faces + Vertices - Edges = 2$).
Since there is no specific question asked in the prompt or visible in the image (such as "How many edges does a dodecahedron have?" or "Which shape has 5 faces?"), I cannot provide a single numerical "Final Answer" to a specific problem.
However, based on the structure of the request, it appears the user may want me to verify the information presented or perhaps identify a discrepancy if one exists. Let's carefully check the mathematical accuracy of the data provided for each shape using Euler's Formula for polyhedra: $F + V - E = 2$ (where F=Faces, V=Vertices, E=Edges).
Step 1: Check the Cuboid
* Given: Faces = 6, Edges = 12, Vertices = 8.
* Check with Euler's Formula: $6 + 8 - 12 = 2$.
* $14 - 12 = 2$. This is correct.
* Description: "A cuboid can be described as a rectangular prism." This is correct.
Step 2: Check the Triangular Prism
* Given: Faces = 5, Edges = 9, Vertices = 6.
* Check with Euler's Formula: $5 + 6 - 9 = 2$.
* $11 - 9 = 2$. This is correct.
* Structure: A triangular prism has 2 triangular bases and 3 rectangular sides. Total faces = 5. Correct.
Step 3: Check the Dodecahedron
* Given: Faces = 12, Edges = 30, Vertices = 20.
* Check with Euler's Formula: $12 + 20 - 30 = 2$.
* $32 - 30 = 2$. This is correct.
* Description: "This shape is one of the five platonic solids." This is correct. A regular dodecahedron is indeed a Platonic solid.
Step 4: Check the Square Based Pyramid
* Given: Faces = 5, Edges = 8, Vertices = 5.
* Check with Euler's Formula: $5 + 5 - 8 = 2$.
* $10 - 8 = 2$. This is correct.
* Structure: A square base (1 face) + 4 triangular sides = 5 faces. Correct.
Conclusion:
All the data presented in the chart is mathematically accurate. There are no errors in the counts of faces, edges, or vertices for any of the shapes listed.
Since no specific question was asked, I will summarize the key data points from the chart as the "answer" to what is likely a study or reference task. If this was a "find the error" task, there are no errors. If it was a "read the table" task, the information is verified.
I will provide a summary of the verified properties as the final output, as this is the most helpful response when no specific question is posed but data validation is implied.
Final Answer:
The information in the chart is correct. Here are the verified properties for each polyhedron:
1. Cuboid: 6 Faces, 12 Edges, 8 Vertices.
2. Triangular Prism: 5 Faces, 9 Edges, 6 Vertices.
3. Dodecahedron: 12 Faces, 30 Edges, 20 Vertices.
4. Square Based Pyramid: 5 Faces, 8 Edges, 5 Vertices.
All shapes satisfy Euler's formula ($Faces + Vertices - Edges = 2$).
Parent Tip: Review the logic above to help your child master the concept of 3d shapes faces edges vertices worksheets with answers.
