Faces, Face Area, and Vertices - SAT Subject Test in Math I
Card 0 of 2
Question
How many vertices does a polyhedron with twenty faces and thirty edges have?
How many vertices does a polyhedron with twenty faces and thirty edges have?
Answer
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.
By Euler's Formula, the relationship between the number of vertices
Set
The polyhedron has tweve vertices.
Compare your answer with the correct one above
Question
How many edges does a polyhedron with nine vertices and eleven faces have?
How many edges does a polyhedron with nine vertices and eleven faces have?
Answer
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.
By Euler's Formula, the relationship between the number of vertices
Set
The polyhedron has eighteen edges.
Compare your answer with the correct one above
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