Question

Euler’s Formula shows the relationship between the number of faces (F), vertices (V), and edges (E) of a polyhedron. Study the answers to the chart above and the answers to the previous problems, and then determine which formula below is Euler’s Formula. (Hint: If the formula works most of the time, but not all of the time, recheck the answers in the chart. The formula should work for every polyhedron.)a.) F + V + 2 = Eb.) F(V) = Ec.) F + V = Ed.) F + V = E + 2

Answer 1

Remember that

Euler's formula state that: In a polyhedron, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

so

V-E+F=2

the answer is option d

Verify each polyhedron

Rectangular prism

F=6, V=8, E=12

8-12+6=2

2=2 is ok

Triangular Pyramid

F=4, V=4, E=6

4-6+4=2

2=2 is ok

Pentagonal prism

F=7, V=10, E=15

10-15+7=2

2=2 is ok

TRiangular prism

F=5, V=6, E=9

6-9+5=2

2=2 is ok