<PRE><B>Question 1141737</B>
&lt;br&gt;
Euler&#39;s Formula: F - E + V = 2.&lt;br&gt;
The polyhedron has 11 faces -- that is given.&lt;br&gt;
The polyhedron has one decagon face and 10 triangle faces.  That is 10+10(3) = 40 edges.  An edge of the polyhedron is where 2 polygon edges meet; so the number of edges of the polyhedron is 40/2 = 20.&lt;br&gt;
Then&lt;br&gt;
{{{11 - 20 + V = 2}}}
{{{V = 11}}}&lt;br&gt;
The polyhedron has 11 vertices.&lt;br&gt;
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While Euler&#39;s Formula is useful for solving many problems, it is not needed here.  A little thinking shows that the polyhedron is a pyramid with a decagon for a base.  The base has 10 vertices; the peak of the pyramid is the only other vertex.&lt;br&gt;
10+1 = 11 vertices.</PRE>