document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=315581>Question 315581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of an equilateral triangle (regular 3-gon) with the given measurement if the apothem is 6inches\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225854 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=225854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The apothem of an equilateral triangle is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ap=%28sqrt%283%29%2F6%29%2AS ALIGN=MIDDLE  ALT=\"Ap=%28sqrt%283%29%2F6%29%2AS\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where S is the length of the side. <BR>\n" );
document.write( "The height of the triangle can be found using Pythagorean therorem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S%2F2%29%5E2%2BH%5E2=S%5E2 ALIGN=MIDDLE  ALT=\"%28S%2F2%29%5E2%2BH%5E2=S%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%2F4%2BH%5E2=S%5E2 ALIGN=MIDDLE  ALT=\"S%5E2%2F4%2BH%5E2=S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2=%283%2F4%29S%5E2 ALIGN=MIDDLE  ALT=\"H%5E2=%283%2F4%29S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=%28sqrt%283%29%2F2%29%2AS ALIGN=MIDDLE  ALT=\"H=%28sqrt%283%29%2F2%29%2AS\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of the triangle is given by,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29bh=%281%2F2%29S%28sqrt%283%29%2F2%29S=%28sqrt%283%29%2F4%29S%5E2 ALIGN=MIDDLE  ALT=\"A=%281%2F2%29bh=%281%2F2%29S%28sqrt%283%29%2F2%29S=%28sqrt%283%29%2F4%29S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the apothem formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ap=%28sqrt%283%29%2F6%29%2AS ALIGN=MIDDLE  ALT=\"Ap=%28sqrt%283%29%2F6%29%2AS\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%286%2Fsqrt%283%29%29Ap ALIGN=MIDDLE  ALT=\"S=%286%2Fsqrt%283%29%29Ap\"   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=%2836%2F3%29A%5E2=12Ap%5E2 ALIGN=MIDDLE  ALT=\"S%5E2=%2836%2F3%29A%5E2=12Ap%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28sqrt%283%29%2F4%29%2812Ap%5E2%29 ALIGN=MIDDLE  ALT=\"A=%28sqrt%283%29%2F4%29%2812Ap%5E2%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=%28sqrt%283%29%2F4%29%2812%2A36%29 ALIGN=MIDDLE  ALT=\"A=%28sqrt%283%29%2F4%29%2812%2A36%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=108sqrt%283%29 ALIGN=MIDDLE  ALT=\"A=108sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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