document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161610>Question 161610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the area of a regular hexagon whose sides are each 12 inches long? (round to the nearest square inch..) (Clue:Draw the figure.) Show all work.<BR>\n" );
document.write( "Thanxs </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119139 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=119139\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> found the answer on the web.<BR>\n" );
document.write( "take the hexagon and draw diagonals through each of the opposite corners.<BR>\n" );
document.write( "this breaks the hexagon up into 6 equilateral triangles.<BR>\n" );
document.write( "each of the sides of these equilateral triangles will be 12 inches long.<BR>\n" );
document.write( "area of a triangle is 1/2 base * height.<BR>\n" );
document.write( "we have the base.<BR>\n" );
document.write( "we need the height.<BR>\n" );
document.write( "take one of the equilateral triangles and drop a perpendicular from opposite side.<BR>\n" );
document.write( "this becomes the height of the triangle.<BR>\n" );
document.write( "the right triangles become 30-60-90 triangles.<BR>\n" );
document.write( "in a 30-60-90 triangle, the sides opposite the angles are in the following ratio:<BR>\n" );
document.write( "side opposite 30 degrees = .5<BR>\n" );
document.write( "side opposite 60 degrees = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "side opposite 90 degrees = 1<BR>\n" );
document.write( "height is side opposite 60 degrees.<BR>\n" );
document.write( "base is side opposite 30 degrees.<BR>\n" );
document.write( "since the base is (1/2)*L and the hypotenuse equals L, the height is equal to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*L<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we now have enough to compute the area of the hexagon.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "area of the hexagon is 6 * the area of each equilateral triangle.<BR>\n" );
document.write( "area of each equilateral triangle is 1/2 * base * height.<BR>\n" );
document.write( "base = 12 <BR>\n" );
document.write( "height = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*12<BR>\n" );
document.write( "formula becomes<BR>\n" );
document.write( "6 * (1/2) * 12 * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*12<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "374.1229744.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "formula for area of the hexagon had become<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%2Asqrt%283%29%29%2F2%29%2AL%5E2 ALIGN=MIDDLE  ALT=\"%28%283%2Asqrt%283%29%29%2F2%29%2AL%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );