Euler’s Formula for Triangular Prism
Euler’s formula states that in any polyhedron, the sum of the number of faces (F) and vertices (V) is equal to two more than the number of edges (E).
Consider a triangular prism. Euler’s formula, which relates the number of faces F, vertices V, and edges E of a polyhedron, is given by:
F + V = E + 2
Now, for the triangular prism:
- The number of faces F is 5.
- The number of vertices V is 6.
- The number of edges E is 9.
Substituting these values into Euler’s formula:
5 + 6 = 9 + 2
This simplifies to:
11 = 11
The result confirms that Euler’s formula is true for the given triangular prism, validating the relationship between the number of faces, vertices, and edges.
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Triangular Prism
Triangular Prism is a three-dimensional geometric shape with two identical triangular faces connected by three rectangular faces. It is one of the classifications of prism. It is named a triangular prism because it has a triangle across its cross-section.
This article covers the meaning of prism and triangular prism, the properties of the prism, the formula of a triangular prism, and the net of a triangular prism. We will also see the types of triangular prism on the basis of uniformity and alignment and verify Euler’s rule for triangular prism.
Table of Content
- What is Prism?
- What is a Triangular Prism?
- Types of Triangular Prism
- Triangular Prism Faces Edges Vertices
- Surface Area of a Triangular Prism
- Volume of Triangular Prism
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