document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203310>Question 1203310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the volume of a hexagonal pyramid is 750 units 3 and the base and the height being 5 units and 10 units respectively, what is the length of apothem of the pyramid? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838773 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838773\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "To start with, the problem is deficient in not stating that the base of the pyramid is a REGULAR hexagon.<br><BR>\n" );
document.write( "Next, it is not clear what \"base... being 5 units\" means.<br><BR>\n" );
document.write( "Finally, the problem is overprescribed when the \"base\", volume, and height of the pyramid are all given and are not consistent.<br><BR>\n" );
document.write( "The only possible way to solve the problem is to ignore one of the given pieces of information.  Since it is not clear what a \"base of 5\" means, I will ignore that.<br><BR>\n" );
document.write( "So my GUESS as to the correct information in the problem is a pyramid with a regular hexagonal base, a height of 10, and a volume of 750.  Then....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29%28B%29%28h%29 ALIGN=MIDDLE  ALT=\"V+=+%281%2F3%29%28B%29%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750+=+%281%2F3%29%28B%29%2810%29 ALIGN=MIDDLE  ALT=\"750+=+%281%2F3%29%28B%29%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=+225 ALIGN=MIDDLE  ALT=\"B=+225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ASSUMING the hexagonal base is regular, each of the equilateral triangles that comprise the base have area 225/6 = 37.5.  In terms of the length a of the apothem, that area (one-half base, times height) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28a%2Fsqrt%283%29%29%28a%29 ALIGN=MIDDLE  ALT=\"A=%28a%2Fsqrt%283%29%29%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37.5=a%5E2%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"37.5=a%5E2%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=37.5%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"a%5E2=37.5%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In exact form, the length of the apothem (with all the assumptions that have been made) is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2837.5%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2837.5%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That's 8.06 to 2 decimal places.<br><BR>\n" );
document.write( "Again, however, note that the presentation of the problem is exceedingly poor....<br><BR>\n" );
document.write( " </SPAN>\n" );
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