F.1 maths question

V + F - E = 2 (Euler's Formula )

Substituting
6 + F - 9 = 2
F = 5

The polyhedron has 5 faces.

P.S. It is easy to find the answer by applying Euler's Formula. To prove the formula is not very difficult but needs to have a good sense of logic and ability to form a mental picture. If you are interested you can visit

http://www.cut-the-knot.org/do_you_know/polyhedra.shtml

If a polyhedron has 6 vertices and 9 edges, it is a triangular prism三角柱體.

vertices/edges/faces fomulas of prism

vertices:number of sides x 2

edges:number of sides x 3

faces:number of sides + 2
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So, as a triangular prism has 3 sides,3+2=5

It has 5 faces

By Euler Formula

F+V-E=2 (F- no of face, V- no of vertex, E- no of Edge)

F+6-9 = 2

F=5

Therefore, the polyhedron has 5 faces.