SAT II Math I : Faces, Face Area, and Vertices

Study concepts, example questions & explanations for SAT II Math I

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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 #2 : 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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