Math Problem Statement

A triangular prism is shown below. How many faces, edges, and vertices does it have?

Solution

To solve the problem, we need to determine the number of faces, edges, and vertices of a triangular prism.

Properties of a Triangular Prism:

  1. Faces: A triangular prism has 5 faces:

    • 2 triangular faces (top and bottom) and
    • 3 rectangular faces connecting the sides of the triangles.
  2. Edges: A triangular prism has 9 edges:

    • 3 edges for each of the two triangular bases (6 edges total),
    • 3 edges connecting the corresponding vertices of the two triangular bases.
  3. Vertices: A triangular prism has 6 vertices:

    • 3 vertices for each triangular base (connected by the edges).

Final Answer:

  • Faces: 5
  • Edges: 9
  • Vertices: 6

Would you like a more detailed explanation or have any related questions?

Here are some related questions you can consider:

  1. How do the formulas for faces, edges, and vertices apply to other prisms?
  2. What is the Euler’s formula for polyhedra, and does it apply here?
  3. How do the shapes of the faces determine the type of prism?
  4. What are some practical examples of triangular prisms in real life?
  5. Can we use the same approach to count these properties for other 3D shapes?

Tip: Remember Euler's formula for polyhedra: VE+F=2V - E + F = 2, where VV is vertices, EE is edges, and FF is faces!

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Math Problem Analysis

Mathematical Concepts

Geometry
Properties of Prisms
Polyhedra

Formulas

Euler's formula for polyhedra: V - E + F = 2

Theorems

Euler's Polyhedron Theorem

Suitable Grade Level

Grades 6-8