How many faces does a pyramid with a hexagonal base have?
What are the shapes of the faces?
How many edges does a pyramid with a hexagonal base have?
How many vertices does a pyramid with a hexagonal base have?
The correct answer and explanation is:
A pyramid with a hexagonal base has 8 faces. The base of the pyramid is a hexagon, and there are 6 triangular faces that connect the vertices of the hexagon to the apex of the pyramid. Therefore, the pyramid has 7 faces in total: 1 hexagonal base and 6 triangular faces.
The shapes of the faces of the pyramid are:
- 1 Hexagonal Face – This is the base of the pyramid.
- 6 Triangular Faces – These are the side faces of the pyramid, each connecting one of the edges of the hexagonal base to the apex.
In terms of edges, a pyramid with a hexagonal base has 12 edges in total. The hexagonal base itself has 6 edges. Each of the 6 vertices of the hexagon is connected to the apex of the pyramid by an additional edge, adding 6 more edges. So, in total, the pyramid has 6 edges from the base and 6 edges connecting the apex to each vertex of the base, for a total of 12 edges.
Finally, the number of vertices in a pyramid with a hexagonal base is 7. There are 6 vertices on the hexagonal base, and the pyramid has 1 more vertex at the apex, which is where all the triangular faces meet. Therefore, the pyramid has 7 vertices in total.
In summary:
- The pyramid has 8 faces: 1 hexagonal face and 6 triangular faces.
- It has 12 edges: 6 from the base and 6 connecting the apex to the base vertices.
- It has 7 vertices: 6 on the base and 1 at the apex.