If a polyhedron has 9 edges and 6 vertices, how many faces does the solid have? A. 4 faces B. 6 faces C. 5 faces D. 7 faces Please select the best answer from the choices provided A B C D

The polyhedran has 5 faces (option C), if a polyhedron has 9 edges and 6 vertices. It is obtained by Euler's theorem.

Step-by-step explanation:

The given is,

                 Polyhedron  

                 9 edges

                 6 vertices

Step:1

                Formula to calculate No. of faces,

                               (1)

               The above equation is known as Polyhedral Formula or Euler's formula.

               Where, F - No. of faces

                            V - No. of vertices

                            E - No. of edges

              From the given,

                            V = 6

                            E = 9

             Equation (1) becomes,

                           F + 6 - 9 = 2

                                 F - 3 = 2

                                      F = 2 + 3

                 No. of face, F = 5

            The solid is Triangular prism, refer attachment.

Result:

         The polyhedran has 5 faces, if a polyhedron has 9 edges and 6 vertices. It is obtained by Euler's theorem.