document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182756>Question 1182756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a regular hexagon, the midpoints of the sides are joined to form a shaded regular hexagon. What fraction of the larger hexagon is shaded? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812831 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I think both the solutions in the link provided by the other tutor are more complicated than necessary.<br><BR>\n" );
document.write( "Let M be the midpoint of side AB of the original regular hexagon.  Then M is one vertex of the smaller inscribed regular hexagon.<br><BR>\n" );
document.write( "Let O be the center of the two hexagons; draw segments OA and OM; triangle AMO is a 30-60-90 right triangle.<br><BR>\n" );
document.write( "OA and OM are corresponding parts of the two hexagons; the ratio of their lengths is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%3A2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%3A2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so the ratio of the areas of the two hexagons is 3:4.<br><BR>\n" );
document.write( "ANSWER: 3:4<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );