document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210279>Question 1210279</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABFE is a square. EBCD is a kite. Find the area of the composite figure.<BR>\n" );
document.write( "https://ibb.co/n8tynFcF </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851835 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=851835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "EB is the diagonal of a square; its length is 12.  Since AEB is an isosceles right triangle, the side length of the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fsqrt%282%29=6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"12%2Fsqrt%282%29=6%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "AEB, FEB, and FBC are all congruent.  Using the standard formula one-half base times height for the area of a triangle, the area of each of those triangles is <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%286sqrt%282%29%29%5E2=%281%2F2%29%2872%29=36 ALIGN=MIDDLE  ALT=\"%281%2F2%29%286sqrt%282%29%29%5E2=%281%2F2%29%2872%29=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note some students will find it easier to view each of those three triangles as one-quarter of a square with side length 12, making the area of each one<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2812%5E2%29=144%2F4=36 ALIGN=MIDDLE  ALT=\"%281%2F4%29%2812%5E2%29=144%2F4=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Either way, the area of ABCE is 3*36 = 108.<br><BR>\n" );
document.write( "Angle EDF is 30 degrees, so triangle EDF is a 30-60-90 right triangle with a short leg of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Using the properties of a 30-60-90 right triangle, the length of DF is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286sqrt%282%29%29%28sqrt%283%29%29=6sqrt%286%29 ALIGN=MIDDLE  ALT=\"%286sqrt%282%29%29%28sqrt%283%29%29=6sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "DF is the altitude of triangle CDE.<br><BR>\n" );
document.write( "Then the area of triangle CDE -- again using the standard formula one-half base time height -- is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286sqrt%282%29%29%286sqrt%286%29%29=36sqrt%2812%29=72sqrt%283%29 ALIGN=MIDDLE  ALT=\"%286sqrt%282%29%29%286sqrt%286%29%29=36sqrt%2812%29=72sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And so the area of the composite figure is<br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2B72sqrt%283%29 ALIGN=MIDDLE  ALT=\"108%2B72sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );