document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087628>Question 1087628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A regular hexagonal pyramid has one lateral edge which measures 10 cm. The length of one side of its base is 6 cm. Find the altitude and the slant height of the given pyramid. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701941 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A regular hexagon can be seen as made of 6 equilateral triangle \"slices\".<BR>\n" );
document.write( "The base of that pyramid can be seen as this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.05%2C1.05%2C-1.05%2C1.05%2C%0D%0Agreen%28triangle%280%2C0%2C1%2C0%2C0.5%2C0.866%29%29%2C%0D%0Agreen%28triangle%280%2C0%2C-1%2C0%2C-0.5%2C0.866%29%29%2C%0D%0Agreen%28triangle%280%2C0%2C-0.5%2C-0.866%2C0.5%2C-0.866%29%29%2C%0D%0Acircle%280%2C0%2C0.02%29%2Clocate%280.4%2C0.1%2Cgreen%286cm%29%29%2C%0D%0Alocate%280.25%2C0.43%2Cgreen%286cm%29%29%2Clocate%280.75%2C0.53%2C6cm%29%2C%0D%0Aline%281%2C0%2C0.5%2C0.866%29%2Cline%281%2C0%2C0.5%2C-0.866%29%2C%0D%0Aline%28-1%2C0%2C-0.5%2C0.866%29%2Cline%28-1%2C0%2C-0.5%2C-0.866%29%2C%0D%0Aline%28-0.5%2C-0.866%2C0.5%2C-0.866%29%2Cline%28-0.5%2C0.866%2C0.5%2C0.866%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A vertical cross-section of that pyramid<BR>\n" );
document.write( "(cutting through the apex and base vertices and center of the base of the pyramid)<BR>\n" );
document.write( "would look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C225%2C-1.05%2C1.05%2C-0.15%2C1.5%2C%0D%0Ared%28triangle%280%2C0%2C1%2C0%2C0%2C1.33%29%29%2C%0D%0Ared%28rectangle%280%2C0%2C0.1%2C0.1%29%29%2C%0D%0Aline%28-1%2C0%2C1%2C0%29%2Clocate%280.03%2C0.6%2Cred%28H%29%29%2C%0D%0Aline%281%2C0%2C0%2C1.33%29%2Cline%28-1%2C0%2C0%2C1.33%29%2C%0D%0Alocate%280.4%2C0.11%2Cgreen%286cm%29%29%2Clocate%280.5%2C0.77%2C10cm%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The Pythagorean theorem says that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28H%29%5E2%2Bgreen%286cm%29%5E2=%2810cm%29%5E2 ALIGN=MIDDLE  ALT=\"red%28H%29%5E2%2Bgreen%286cm%29%5E2=%2810cm%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the altitude of the pyramid measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28H%29=sqrt%28%2810cm%29%5E2-green%286cm%29%5E2%29=highlight%288cm%29 ALIGN=MIDDLE  ALT=\"red%28H%29=sqrt%28%2810cm%29%5E2-green%286cm%29%5E2%29=highlight%288cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "\n" );
document.write( "The triangles that form the sides of the pyramid}} are isosceles triangles with 6 cm bases and 10 cm sides.<BR>\n" );
document.write( "Their altitude is the slant height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the pyramid,<BR>\n" );
document.write( "and it can also be calculated, using the Pythagorean theorem, as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2%2B%283cm%29%5E2=%2810cm%29%5E2 ALIGN=MIDDLE  ALT=\"s%5E2%2B%283cm%29%5E2=%2810cm%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2%2B9cm%5E2=100cm%5E2 ALIGN=MIDDLE  ALT=\"s%5E2%2B9cm%5E2=100cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2=100cm%5E2-9cm%5E2 ALIGN=MIDDLE  ALT=\"s%5E2=100cm%5E2-9cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2=91cm%5E2 ALIGN=MIDDLE  ALT=\"s%5E2=91cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=highlight%28sqrt%2891%29%29 ALIGN=MIDDLE  ALT=\"s=highlight%28sqrt%2891%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm=about ALIGN=MIDDLE  ALT=\"cm=about\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289.54cm%29 ALIGN=MIDDLE  ALT=\"highlight%289.54cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );