Answer:
56
Step-by-step explanation:
Euler theorem is a theorem used to show the relationship between the face, vertices and edge of a three dimensional shape (polyhedron)
Euler theorem is given as:
Face + vertex = Edge + 2
We can prove this theorem using the table attached.
For triangular prism: 5 + 6 = 9 + 2
For rectangular prism: 6 + 8 = 12 + 2
For pentagon prism: 7+ 10 = 15 + 2
For hexagonal prism: 8 + 12 = 18 + 2
The relationship between the vertex and face is:
vertex = face + (face - 4)
Therefore, for a prism with 30 sides, that is 30 faces, we have:
vertices = 30 + (30 - 4) = 30 + 26 = 56
