Draw a triangular prism and verify Euler’s Formula.

To verify Euler's formula for a triangular prism, we need to follow these steps:

1. Understanding Euler's Formula: Euler's formula for polyhedra states that: V - E + F = 2 where:

V = number of vertices,
E = number of edges,
F = number of faces.
2. Triangular Prism: A triangular prism consists of two parallel triangular faces and three rectangular lateral faces. Let's first define the number of vertices, edges, and faces for a triangular prism.

Vertices (V): A triangular prism has two triangular faces, and each triangle has 3 vertices. Since the two triangles are parallel, the total number of vertices is: V = 6 (3 vertices from the first triangle + 3 vertices from the second triangle).

Edges (E): Each triangle has 3 edges. There are 3 rectangular faces connecting the corresponding vertices of the two triangles, and each rectangle has 2 edges. So, the total number of edges is: E = 9 (3 edges from the first triangle + 3 edges from the second triangle + 3 edges from the rectangles).

Faces (F): A triangular prism has 2 triangular faces and 3 rectangular faces, so the total number of faces is: F = 5 (2 triangular faces + 3 rectangular faces).

3. Verify Euler’s Formula: Now, using Euler's formula, we can check: V - E + F = 6 - 9 + 5 = 2.

This satisfies Euler’s formula.

Conclusion: Euler’s formula is verified for a triangular prism since the calculation 6 - 9 + 5 equals 2, confirming that Euler’s formula holds true for this polyhedron.