document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42824>Question 42824</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! I'm trying to figure out a problem with a hexagon. I need to find the side of a regular hexagon if the it is 18 inches apart from midpoint to midpoint. Any help would be greatly appreciated!<BR>\n" );
document.write( "Thankyou! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27920 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your statement of the problem is not very clear.<BR>\n" );
document.write( "I assume, what you meant is: The side of a regular hexagon in which the distance between the opposite sides is 18\".\r<BR>\n" );
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document.write( "See the regular hexagon ABCDEF below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0Aline%286%2C0%2C3%2C5.2%29%2C%0D%0Aline%286%2C0%2C3%2C-5.2%29%2C%0D%0Aline%28-6%2C0%2C-3%2C5.2%29%2C%0D%0Aline%28-6%2C0%2C-3%2C-5.2%29%2C%0D%0Aline%283%2C5.2%2C-3%2C5.2%29%2C%0D%0Aline%283%2C-5.2%2C-3%2C-5.2%29%2C%0D%0Alocate%286%2C0%2CA%29%2C%0D%0Alocate%283%2C5.2%2CB%29%2C%0D%0Alocate%28-3%2C5.2%2CC%29%2C%0D%0Alocate%28-6%2C0%2CD%29%2C%0D%0Alocate%28-3%2C-5.2%2CE%29%2C%0D%0Alocate%283%2C-5.2%2CF%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "According to the problem the distance between sides AB & DE, BC & EF and CD & FA is 18\" and we are required to find length AB or any other side.\r<BR>\n" );
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document.write( "Join B and F with a straight line. Then drop a perpendicular to BF from A intersecting BF at G.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0Aline%286%2C0%2C3%2C5.2%29%2C%0D%0Aline%286%2C0%2C3%2C-5.2%29%2C%0D%0Aline%28-6%2C0%2C-3%2C5.2%29%2C%0D%0Aline%28-6%2C0%2C-3%2C-5.2%29%2C%0D%0Aline%283%2C5.2%2C-3%2C5.2%29%2C%0D%0Aline%283%2C-5.2%2C-3%2C-5.2%29%2C%0D%0Alocate%286%2C0%2CA%29%2C%0D%0Alocate%283%2C5.2%2CB%29%2C%0D%0Alocate%28-3%2C5.2%2CC%29%2C%0D%0Alocate%28-6%2C0%2CD%29%2C%0D%0Alocate%28-3%2C-5.2%2CE%29%2C%0D%0Alocate%283%2C-5.2%2CF%29%2C%0D%0Aline%283%2C5.2%2C3%2C-5.2%29%2C%0D%0Aline%286%2C0%2C3%2C0%29%2C%0D%0Alocate%283%2C0%2CG%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, in triangle ABF,<BR>\n" );
document.write( "BF = 18\",<BR>\n" );
document.write( "< BAF = <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;\" > [since each internal angle of a regular hexagon is <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;\" >]\r<BR>\n" );
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document.write( "Clearly, triangle ABG and triangle AFG are congruent.<BR>\n" );
document.write( "So, < BAG = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >< BAF = <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;\" > and BG = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >BF = 9\".\r<BR>\n" );
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document.write( "Now, in triangle ABG,<BR>\n" );
document.write( "< AGB = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%5Eo ALIGN=MIDDLE  ALT=\"90%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > [since AG is perpendicular to BF]<BR>\n" );
document.write( "So in right angled triangle AGB,<BR>\n" );
document.write( "sin(< BAG) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BG%2FAB ALIGN=MIDDLE  ALT=\"BG%2FAB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or sin<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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2FAB ALIGN=MIDDLE  ALT=\"9%2FAB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or AB = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Fsin%2860%5Eo%29 ALIGN=MIDDLE  ALT=\"9%2Fsin%2860%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\" = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%28sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"9%2F%28sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\" = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6sqrt%283%29 ALIGN=MIDDLE  ALT=\"6sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\" = 10.4\" (approx)\r<BR>\n" );
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document.write( "Thus the reqd. side of the regular hexagon is approximately 10.4 inches. </SPAN>\n" );
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