Math Problem Statement

Number of faces, edges, vertex of a triangular prism and a square-based pyramid

Solution

Here’s the breakdown for both 3D shapes:

Triangular Prism

  • Faces: 5 (2 triangular + 3 rectangular)
  • Edges: 9
  • Vertices: 6

Square-based Pyramid

  • Faces: 5 (1 square + 4 triangular)
  • Edges: 8
  • Vertices: 5

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Related Questions:

  1. How do you derive Euler's formula for polyhedra?
  2. What are the real-world applications of a triangular prism?
  3. How can you calculate the surface area of a square-based pyramid?
  4. What is the difference between a pyramid and a prism?
  5. How do you find the volume of a triangular prism?

Tip:

To verify the number of faces, edges, and vertices, use Euler’s formula for polyhedra:
VE+F=2V - E + F = 2
where VV = vertices, EE = edges, and FF = faces.

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Math Problem Analysis

Mathematical Concepts

Geometry
Polyhedra
3D Shapes

Formulas

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

Theorems

Euler's polyhedron formula

Suitable Grade Level

Grades 6-8