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 PQR\triangle PQR and STU\triangle STU 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 (PRSTPRST, RQUTRQUT, and PQSUPQSU).
  • Edges: There are 9 edges: PQPQ, PRPR, QRQR, STST, SUSU, TUTU, PSPS, RTRT, and QUQU.
  • Vertices: The polyhedron has 6 vertices: PP, QQ, RR, SS, TT, and UU.

Would you like more details or have any questions?

Here are 5 related questions for further learning:

  1. How would you calculate the surface area of this triangular prism?
  2. What is the formula for the volume of a triangular prism?
  3. How can you distinguish between a prism and a pyramid?
  4. How does the number of faces, edges, and vertices change for different prisms?
  5. 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