Question

verify Euler formula for the polyhedron

Answer 1

This theorem involves Euler's polyhedral formula (sometimes called Euler's formula). Today we would state this result as: The number of vertices V, faces F, and edges E in a convex 3-dimensional polyhedron, satisfy V + F - E = 2.

Answer 2

Answer:

Step-by-step explanation:

For any polyhedron, Number of Faces + Number of Vertices - Number of Edges = 2. This is Euler's formula.

In a Pentagonal Prism,

Number of Faces = 7 (1 is at top, 1 is at bottom and 5 are lateral)

Number of Vertices = 10 (5 are at the top and 5 are at the bottom)

Number of Edges = 15 (5 are at the top, 5 are on the lateral sides and 5 are at the bottom)

So, F + V - E = 2

∴ 7 + 10 - 15

17 - 15

= 2

Hence verified