Which of the following statements is true about the prism below?

1. The bases of the prism are DAEH and DABC.
   Incorrect. The bases of the prism are always opposite each other.
2. The opposite faces of the prism are parallel.
   Correct! Opposite faces of a prism are always parallel.
3. The edges of the prism are DA, DH, HE, EA, GF, FB, BC, and CG.
   Incorrect. These are some of the edges, but not ALL of the edges.
4. The prism has 12 vertices.
   Incorrect. Vertices are the points where two or more edges intersect. There are 12 edges in this prism, but not 12 vertices.

Use Euler's Formula to determine the number of faces, edges and vertices in a prism with a base that is a dodecagon.

V – E + F = 2

1. F = 14
   E = 36
   V = 24
   Correct! A dodecagon is a 12-sided figure. So a prism whose bases are dodecagons has 12 lateral faces and 2 bases for a total of 14 faces, 24 vertices, and 36 edges.
2. F = 14
   V = 24
   E = 36
   Incorrect. Check your formula again, it appears you mixed up the number of edges and vertices in the prism.
3. F = 12
   E = 30
   V = 20
   Incorrect. A dodecagon is a 12 sided figure so the prism has to have 12 lateral faces, but it also has 2 bases. The bases of a prism are also faces.
4. F = 11
   E = 24
   V = 13
   Incorrect. A prism has two bases and it appears you found the faces, edges and vertices for a pyramid with a dodecagon base.

Which of the following figures has 10 faces, 16 vertices, and 24 edges?

A. octagonal pyramid
Incorrect. An octagonal pyramid only has 9 faces – 8 lateral faces and 1 base.

B. octagonal prism
Correct! An octagonal prism has 10 faces – 8 lateral faces and 2 bases, 16 vertices, and 24 edges.

C. hexagonal prism
Incorrect. A hexagonal prism has 8 faces – 6 lateral faces and 2 bases.

D. nonagonal pyramid
Incorrect. A nonagonal pyramid has 10 faces – 9 lateral faces and 1 base – but it only has 10 vertices.

Which of the following figures has 8 faces, 6 vertices, and 12 edges?

1. 
   Correct! This octahedron has 8 faces, 6 vertices, and 12 edges.
2. 
   Incorrect. This cube has 6 faces.
3. 
   Incorrect. This dodecahedron has 12 faces.
4. 
   Incorrect. This icosahedron has 20 faces.