Question

The Swiss mathematician Leonhard Euler and the French mathematician Rene Descartes both discovered a pattern in the numbers of edges, vertices, and faces of polyhedrons. Solve problems 8-10. 8. Complete the table. Describe a pattern in the table. Polyhedron Faces (F) Vertices (V) F + V Edges (E) Triangular Pyramid Rectangular Pyramid Triangular Prism Enter your answer in the edit fields and then click Check Answer. 3 parts remaining Clear All Check Answer Review progress Question 5 of 6 Back Next → e to search JO

Answer 1

Faces | Vertices | F+V | Edges

Triangular Pyramid 4 4 8 6

Rectangular Pyramid 5 5 10 8

Triangular Prism 5 6 11 9

1) Since we can set a relationship based on the Euler equation: V +F= E+2

And then we can fill in the table:

Faces | Vertices | F+V | Edges

Triangular Pyramid 4 4 8 6

Rectangular Pyramid 5 5 10 8

Triangular Prism 5 6 11 9

2) Using the Euler's equation to find the missing information:

Rectangular Pyramid

V + F = E +2

V +5 = 8 +2

V= 10-5

V =5

Triangular Prism

V+F =E+2

6 + F =9+2

F = 11 -6

F = 5

3) Hence, the answer is:

Faces | Vertices | F+V | Edges

Triangular Pyramid 4 4 8 6

Rectangular Pyramid 5 5 10 8

Triangular Prism 5 6 11 9