Question

look at the shape.
pick all the ways to describe the shape.
the shape has 8 vertices.
the shape has 6 edges.
the shape has 5 faces.

Explanation:

Identify the 3D shape

The given shape is a triangular prism, which has two parallel triangular bases and three rectangular lateral faces.

Count the vertices, edges, and faces

• Vertices: \(2 \times 3 = 6\) vertices.
• Edges: \(3 \text{ (base 1)} + 3 \text{ (base 2)} + 3 \text{ (lateral)} = 9\) edges.
• Faces: \(2 \text{ (triangular bases)} + 3 \text{ (rectangular faces)} = 5\) faces.

Evaluate the given statements

• "The shape has 8 vertices" is incorrect (it has 6).
• "The shape has 6 edges" is incorrect (it has 9).
• "The shape has 5 faces" is correct.

Answer:

• The shape has 8 vertices.
• The shape has 6 edges.
• The shape has 5 faces. (Correct answer)