Math Problem Statement

To which polyhedron does this net belong?

Solution

The question asks to identify the polyhedron that corresponds to the given net. The net shown in the top part of the image is a series of equilateral triangles arranged to form a closed 3D shape when folded.

Analyzing each option:

  1. Option (a) shows an octahedron, which has eight equilateral triangular faces. This net does not correspond to the structure of an octahedron.
  2. Option (b) is a tetrahedron, which has four triangular faces. This net could correspond to a tetrahedron if folded correctly.
  3. Option (c) shows a triangular prism, which has rectangular faces in addition to triangular bases. The net provided lacks any rectangular faces, so this is not a match.
  4. Option (d) depicts a pentagonal pyramid, which has a pentagonal base and triangular faces. This net also does not match a pentagonal pyramid.

The correct answer is therefore (b), the tetrahedron, as it matches the triangular structure and can be folded into a shape with four triangular faces.

Would you like further clarification on the shapes involved or a deeper breakdown?

Related Questions

  1. What are the characteristics of a tetrahedron?
  2. How many faces does an octahedron have?
  3. What types of polyhedra have triangular faces?
  4. How can you determine if a net corresponds to a specific polyhedron?
  5. What are some examples of nets that can form a cube?

Tip: When matching nets to polyhedra, count the faces and examine the shape and layout of the net to determine if it can be folded to form the intended 3D shape.

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Math Problem Analysis

Mathematical Concepts

Polyhedrons
Nets of 3D shapes
Geometry

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8