Question

Use Euler's Formula to find the number of vertices in a polyhedron with nine faces: one octagon and eight triangles.

Answer 1

The number of vertices in the polyhedron is
`9`

Explanation:

we know that

The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

so

`V - E + F = 2`

In this problem we have

`F=9, E=8+8=16`

substitute and solve for V

`V - 16 +9 = 2`

`V = 2+7=9`