document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196955>Question 196955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> make a regular hexagon of sides as you wish and divide them into six equilateral   triangles and find its area ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147729 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=147729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Tahoma\" 1.5><BR>\n" );
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document.write( "We draw the hexagon:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-3%2C3%2Cline%282%2C2%2C4%2C0%29%2Cline%284%2C0%2C2%2C-2%29%2Cline%282%2C-2%2C-2%2C-2%29%2Cline%28-2%2C-2%2C-4%2C0%29%2Cline%28-4%2C0%2C-2%2C2%29%2Cline%28-2%2C2%2C2%2C2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-3%2C3%2Cline%282%2C2%2C4%2C0%29%2Cline%284%2C0%2C2%2C-2%29%2Cline%282%2C-2%2C-2%2C-2%29%2Cline%28-2%2C-2%2C-4%2C0%29%2Cline%28-4%2C0%2C-2%2C2%29%2Cline%28-2%2C2%2C2%2C2%29%2Cline%28-2%2C2%2C2%2C-2%29%2Cline%282%2C2%2C-2%2C-2%29%2Cline%28-4%2C0%2C4%2C0%29%2Cgreen%28locate%28-1%2C.5%2C60%5Eo%29%29%2Cgreen%28locate%280%2C.8%2C60%5Eo%29%29%2Cgreen%28locate%28.8%2C.6%2C60%5Eo%29%29%2Cgreen%28locate%28.7%2C-.1%2C60%5Eo%29%29%2Cgreen%28locate%28-.5%2C-.4%2C60%5Eo%29%29%2Cgreen%28locate%28-1%2C-.1%2C60%5Eo%29%29%2Cred%28line%28-5%2C0%2C5%2C0%29%29%2Cred%28line%280%2C3%2C0%2C-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The interior angles in the center measure 60 deg. => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo%2F6=60%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo%2F6=60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Being Equilateral, all interior angles are 60 deg.\r<BR>\n" );
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document.write( "Let us isolate 1 Triangle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-3%2C3%2Cline%28-2%2C2%2C-4%2C0%29%2Cline%28-4%2C0%2C0%2C0%29%2Cline%280%2C0%2C-2%2C2%29%2Cred%28line%28-5%2C0%2C5%2C0%29%29%2Cred%28line%280%2C3%2C0%2C-3%29%29%2Cred%28line%28-2%2C2%2C-2%2C0%29%29%2Cred%28locate%28-2.3%2C1.4%2Ch%29%29%2Cred%28locate%28-3%2C.3%2Cb%29%29%2Cgreen%28locate%28-3.5%2C1.5%2C2%29%29%2Cgreen%28locate%28-.5%2C1.5%2C2%29%29%2Cgreen%28locate%28-2%2C-.3%2C2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As you can see, we make all sides equal to <font color=blue>2 units.</font>\r<BR>\n" );
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document.write( "Woking Eqn, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BT%5D=%281%2F2%29%28b%29%28h%29 ALIGN=MIDDLE  ALT=\"A%5BT%5D=%281%2F2%29%28b%29%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28b=%281%2F2%29%282%29=red%281%29%29 ALIGN=MIDDLE  ALT=\"system%28b=%281%2F2%29%282%29=red%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving \"h\" via Pyth Theorem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2=b%5E2%2Bh%5E2 ALIGN=MIDDLE  ALT=\"2%5E2=b%5E2%2Bh%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=2%5E2-b%5E2=2%5E2-1%5E1=4-1 ALIGN=MIDDLE  ALT=\"h%5E2=2%5E2-b%5E2=2%5E2-1%5E1=4-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28h=sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"red%28h=sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Going Back Working Eqn:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BT%5D=%281%2F2%29%281%29%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"A%5BT%5D=%281%2F2%29%281%29%28sqrt%283%29%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%5BT%5D=%281%2F2%29%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"A%5BT%5D=%281%2F2%29%28sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, sq.units\r<BR>\n" );
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document.write( "And there are <font color=blue>2 Right Triangles </font>for 1 Equilateral Triangle. Therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28A%5BT%5D%29=cross%282%29%2A%281%2Fcross%282%29%29%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"2%28A%5BT%5D%29=cross%282%29%2A%281%2Fcross%282%29%29%28sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"red%28sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----> There are <font color=blue>6 Equilateral Triangles</font>:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28red%28%286%29%28sqrt%283%29%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%28red%28%286%29%28sqrt%283%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > sq.units (Answer)\r<BR>\n" );
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document.write( "We can also do it by Trigo function since we know the interior angles.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-3%2C3%2Cline%28-2%2C2%2C-4%2C0%29%2Cline%28-4%2C0%2C0%2C0%29%2Cline%280%2C0%2C-2%2C2%29%2Cred%28line%28-5%2C0%2C5%2C0%29%29%2Cred%28line%280%2C3%2C0%2C-3%29%29%2Cred%28line%28-2%2C2%2C-2%2C0%29%29%2Cred%28locate%28-2.3%2C1.4%2Ch%29%29%2Cgreen%28locate%28-3.5%2C1.5%2C2%29%29%2Cgreen%28locate%28-.5%2C1.5%2C2%29%29%2Cgreen%28locate%28-2%2C-.3%2C2%29%29%2Cgreen%28locate%28-3.6%2C.5%2C60%5Eo%29%29%2Cred%28locate%28-2.8%2C.3%2Cb%29%29%2Cgreen%28locate%28-.8%2C.5%2C60%5Eo%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin60%5Eo=opp%2Fhyp=h%2F2 ALIGN=MIDDLE  ALT=\"sin60%5Eo=opp%2Fhyp=h%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%28sin60%5Eo%29%282%29 ALIGN=MIDDLE  ALT=\"h=%28sin60%5Eo%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28h=sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"red%28h=sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos60%5Eo=adj%2Fhyp=b%2F2 ALIGN=MIDDLE  ALT=\"cos60%5Eo=adj%2Fhyp=b%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%28cos60%5Eo%29%282%29=0.50%282%29 ALIGN=MIDDLE  ALT=\"b=%28cos60%5Eo%29%282%29=0.50%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28b=1%29 ALIGN=MIDDLE  ALT=\"red%28b=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Just do the same we did for Area of Triangle above.\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Jojo</font>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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