A pentagonal pyramid has

The correct option is six vertices and six faces.

To understand the properties of a pentagonal pyramid, we can analyze its structure by looking at its base and its lateral (side) faces:

1. Base: A pentagonal pyramid has a pentagon as its base. A pentagon is a flat shape with 5 vertices and 5 edges.

2. Apex: The pyramid has a single point at the top where all the triangular side faces meet, known as the apex.

Now, let's calculate the total number of vertices and faces step-by-step:

Vertices:
The total number of vertices is the sum of the vertices of the pentagonal base and the single apex vertex at the top.

$\text{Number of vertices}=5+1=6$

Faces:
The total number of faces is the sum of the base face and the lateral faces. Since the base has 5 edges, there are 5 triangular lateral faces connecting the base to the apex. Adding the 1 pentagonal base face gives the total.

$\text{Number of faces}=1+5=6$

Thus, a pentagonal pyramid has exactly 6 vertices and 6 faces.