Find number of faces of a polyhedron, which has 27 edges and 17 vertices.



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2 thoughts on “Find number of faces of a polyhedron, which has 27 edges and 17 vertices.<br /><br /><br /><br />I will make u as brainelist ​”

1. Answer :–

   • Number of faces = 12

   To Find :–

   • Number of faces of a polyhedron.

   Given :–

   • Number of edges = 27

   • Number of vertices = 17

   Step By Step Explanation :–

   In this question we already know the number of edges and number of vertices = 27 and 17 respectively. We need to find the number of faces.

   We can find the number of faces using Euler’s formula that is ⤵

   [tex] {\bf{ \red{Faces + Vertices – Edges = 2}}}[/tex]

   By substituting the values ⤵

   [tex] \implies\sf \: Faces + 17 – 27 = 2 \\ \\ \implies\sf Faces – 10 = 2 \\ \\ \implies\sf Faces = 2 + 10 \\ \\ \implies\sf Faces = 12[/tex]

   Therefore number of faces = 12

   Check :–

   L. H. S.

   => 12 + 17 – 27

   => 29 – 27

   => 2

   R. H. S.

   => 2

   Therefore L. H. S. = R. H. S.

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2. Answer:

   12

   Step-by-step explanation:

   In geometry, there is a really nifty, simple and extremely useful thing called Euler’s formula, and it looks like this:

   V−E+F=2 , where.

   V= the number of vertices of a polyhedron.

   E= the number of edges of a polyhedron.

   F= the number of faces of a polyhedron.

   V=17 , E=27 , F=? .

   V-E+F=2

   17-27+F=2

   F=2+27-17

   F=12

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