### All SAT II Math I Resources

## Example Questions

### Example Question #1 : Faces, Face Area, And Vertices

How many vertices does a polyhedron with twenty faces and thirty edges have?

**Possible Answers:**

**Correct answer:**

Explanation:

By Euler's Formula, the relationship between the number of vertices , the number of faces , and the number of edges of a polyhedron is

Set and , and solve for :

The polyhedron has tweve vertices.

### Example Question #1 : Faces, Face Area, And Vertices

How many edges does a polyhedron with nine vertices and eleven faces have?

**Possible Answers:**

**Correct answer:**

Explanation:

By Euler's Formula, the relationship between the number of vertices , the number of faces , and the number of edges of a polyhedron is

Set and and solve for :

The polyhedron has eighteen edges.

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