Math Problem Statement
Determine whether each solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.
Solution
The solid depicted in the image is a polyhedron. It appears to be a triangular prism, as it has two triangular bases and three rectangular lateral faces.
Here are the details:
- Bases: The two triangular faces and are the bases of the triangular prism.
- Faces: The prism has 5 faces in total – 2 triangular bases (as mentioned above) and 3 rectangular faces (, , and ).
- Edges: There are 9 edges: , , , , , , , , and .
- Vertices: The polyhedron has 6 vertices: , , , , , and .
Would you like more details or have any questions?
Here are 5 related questions for further learning:
- How would you calculate the surface area of this triangular prism?
- What is the formula for the volume of a triangular prism?
- How can you distinguish between a prism and a pyramid?
- How does the number of faces, edges, and vertices change for different prisms?
- What are the key characteristics that define a polyhedron?
Tip: To check whether a solid is a polyhedron, ensure that all faces are flat polygons, and there are no curved surfaces.
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Math Problem Analysis
Mathematical Concepts
Geometry
Polyhedrons
Three-dimensional shapes
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9