Question

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

Answer 1

Answer:

The number of vertices in the polyhedron is $9$  

Step-by-step 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

$V - 16 +9 = 2$

$V = 2+7=9$