Math Problem Statement

Name each shape and describe it by its faces, vertices, and edges.

Solution

Let’s analyze each shape in the image by naming them and describing their faces, vertices, and edges.

Shape Descriptions:

  1. Shape (a) appears to be a triangular prism.

    • Faces: 5 (two triangular faces and three rectangular faces)
    • Vertices: 6
    • Edges: 9
  2. Shape (b) looks like a hexagonal prism.

    • Faces: 8 (two hexagonal faces and six rectangular faces)
    • Vertices: 12
    • Edges: 18
  3. Shape (c) resembles a square pyramid.

    • Faces: 5 (one square base and four triangular faces)
    • Vertices: 5
    • Edges: 8

Would you like further details on any specific shape?


Relative Questions:

  1. What is the difference between a prism and a pyramid?
  2. How do we calculate the number of edges in a 3D shape?
  3. What are the properties of regular polyhedra?
  4. How do different prisms vary based on their base shape?
  5. How do you determine the number of faces, vertices, and edges using Euler’s formula?

Tip:

To easily identify the type of a prism, look at the shape of its two parallel faces (bases); this shape determines the type of prism.

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Math Problem Analysis

Mathematical Concepts

Geometry
3D Shapes
Faces, Vertices, and Edges of Polyhedra

Formulas

Euler's Formula (V - E + F = 2 for polyhedra)

Theorems

Euler's Polyhedron Formula

Suitable Grade Level

Grades 5-7