document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066618>Question 1066618</A>: <I><SPAN STYLE=\"word-break: break-all;\"> start with an equilateral triangle ABC of a side of 2 units and construct three outward-pointing squares ABPQ, BCTU, CARS and the three sides AB, BC and CA. what is the area of the hexagon PQRSTU?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681839 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=681839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The hexagon is made up of<BR>\n" );
document.write( "1 central equilateral triangle of side length 2,<BR>\n" );
document.write( "3 squares of side length 2, and<BR>\n" );
document.write( "3 isosceles triangles sharing sides of length 2 with the squares.<BR>\n" );
document.write( "The surface area of each square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2=4 ALIGN=MIDDLE  ALT=\"2%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The surface area of any triangle ABC can be calculated as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2AAB%2ABC%2Asin%28B%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2AAB%2ABC%2Asin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For the central, equilateral triangle ABC,<BR>\n" );
document.write( "all sides have equal length, and all angles have the same measure:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=BC=AC=2 ALIGN=MIDDLE  ALT=\"AB=BC=AC=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=B=C=60%5Eo ALIGN=MIDDLE  ALT=\"A=B=C=60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28ABC%29=%281%2F2%29%2A2%2A2%2Asin%2860%5Eo%29=%281%2F2%29%2A2%2A2%2A%28sqrt%283%29%2F2%29=sqrt%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The angle between the squares measures<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%5Eo=360%5Eo-%2890%5Eo%2B60%5Eo%2B90%5Eo%29 ALIGN=MIDDLE  ALT=\"120%5Eo=360%5Eo-%2890%5Eo%2B60%5Eo%2B90%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because it completes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > when added to<BR>\n" );
document.write( "the right angles of two squares,<BR>\n" );
document.write( "plus a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%5Eo ALIGN=MIDDLE  ALT=\"60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle of the central equilateral triangle.<BR>\n" );
document.write( "So each of the three outside isosceles triangles have<BR>\n" );
document.write( "two sides of length 2 flanking an angle measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%5Eo ALIGN=MIDDLE  ALT=\"120%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the area of each of those 3 isosceles triangles is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A2%2A2%2Asin%28120%5Eo%29=%281%2F2%29%2A2%2A2%2A%28sqrt%283%29%2F2%29=sqrt%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since the area of the hexagon is the sum of the areas of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > squares, each with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28square%29=4 ALIGN=MIDDLE  ALT=\"area%28square%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangles, each with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28triangle%29=sqrt%283%29 ALIGN=MIDDLE  ALT=\"area%28triangle%29=sqrt%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=area%28hexagon%29=3%2A4%2B4%2Asqrt%283%29=highlight%2812%2B4sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"area%28hexagon%29=3%2A4%2B4%2Asqrt%283%29=highlight%2812%2B4sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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