document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141737>Question 1141737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Euler’s Formula to find the number of vertices in the polyhedron with 11 faces, 1 decagon, and 10 triangles.<BR>\n" );
document.write( "a. 11<BR>\n" );
document.write( "b. 22<BR>\n" );
document.write( "c. 6<BR>\n" );
document.write( "d. 10 </SPAN>\n" );
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document.write( "Euler's Formula: F - E + V = 2.<br><BR>\n" );
document.write( "The polyhedron has 11 faces -- that is given.<br><BR>\n" );
document.write( "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.<br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+-+20+%2B+V+=+2 ALIGN=MIDDLE  ALT=\"11+-+20+%2B+V+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+11 ALIGN=MIDDLE  ALT=\"V+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The polyhedron has 11 vertices.<br><BR>\n" );
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document.write( "While Euler'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.<br><BR>\n" );
document.write( "10+1 = 11 vertices. </SPAN>\n" );
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