document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=823877>Question 823877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCD IS A PARALLELOGRAM.TRIANGLE DEC IS DRAWN SUCH THAT BE=1/3 AE.SUM OF THE AREAS OF TRIANGLES ADE AND BEC IS? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496016 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5345)</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=496016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the problem does not state any side measurements (just a ratio), the most that we could do is calculate that sum of areas relative to the area of the parallelogram.<BR>\n" );
document.write( "Without a picture, I am not quite sure I can interpret the situation intended, but I will try.<BR>\n" );
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document.write( "We could calculate that sum of areas as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2Aarea ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Aarea\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=of ALIGN=MIDDLE  ALT=\"of\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABCD ALIGN=MIDDLE  ALT=\"ABCD\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the situation below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-1%2C14%2C-1%2C9%2C%0D%0Aline%280%2C0%2C3%2C8%29%2Cline%2813%2C8%2C3%2C8%29%2C%0D%0Aline%280%2C0%2C10%2C0%29%2Cline%2813%2C8%2C10%2C0%29%2C%0D%0Aarrow%280%2C0%2C4%2C0%29%2Carrow%283%2C8%2C7%2C8%29%2C%0D%0Aarrow%280%2C0%2C1.5%2C4%29%2Carrow%2810%2C0%2C11.5%2C4%29%2C%0D%0Alocate%28-.2%2C0%2CA%29%2Clocate%282.8%2C8.8%2CB%29%2C%0D%0Alocate%289.8%2C0%2CD%29%2Clocate%2813%2C8.8%2CC%29%2C%0D%0Alocate%284.8%2C0%2Cb%29%2Clocate%287.8%2C8%2Cb%29%2Clocate%288.8%2C4.4%2Ch%29%2C%0D%0Aarrow%289%2C5%2C9%2C8%29%2Carrow%289%2C3%2C9%2C0%29%2C%0D%0Agreen%28line%28-1%2C6%2C14%2C6%29%29%2Cgreen%28arrow%2810%2C6%2C10%2C8%29%29%2C%0D%0Agreen%28arrow%2810%2C8%2C10%2C6%29%29%2Clocate%2810.1%2C8%2Cgreen%28h%2F4%29%29%2C%0D%0Ared%28circle%282.25%2C6%2C0.15%29%29%2Clocate%282.25%2C6%2CE%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "In that case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BE=%281%2F3%29AE ALIGN=MIDDLE  ALT=\"BE=%281%2F3%29AE\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area ALIGN=MIDDLE  ALT=\"area\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=of ALIGN=MIDDLE  ALT=\"of\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BCE=%281%2F2%29b%2A%28h%2F4%29 ALIGN=MIDDLE  ALT=\"BCE=%281%2F2%29b%2A%28h%2F4%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 ALIGN=MIDDLE  ALT=\"area\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=of ALIGN=MIDDLE  ALT=\"of\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ADE=%281%2F2%29b%2A%283h%2F4%29 ALIGN=MIDDLE  ALT=\"ADE=%281%2F2%29b%2A%283h%2F4%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 ALIGN=MIDDLE  ALT=\"area\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=of ALIGN=MIDDLE  ALT=\"of\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABCD=b%2Ah ALIGN=MIDDLE  ALT=\"ABCD=b%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "area of ADE + area of BCE =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29b%2A%283h%2F4%29%2B%281%2F2%29b%2A%28h%2F4%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29b%2A%283h%2F4%29%2B%281%2F2%29b%2A%28h%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "area of ADE + area of BCE =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29b%2A%283h%2F4%2Bh%2F4%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29b%2A%283h%2F4%2Bh%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "area of ADE + area of BCE =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29b%2Ah%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29b%2Ah%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It really does not matter what fraction of AE is BE,<BR>\n" );
document.write( "because the heights of ADE and BCE would add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > anyway.\r<BR>\n" );
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document.write( "It really does not matter where E is located, as long as it is between the lines AD and BC,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-1%2C14%2C-0.8%2C9.2%2C%0D%0Aline%280%2C0%2C3%2C8%29%2Cline%2813%2C8%2C3%2C8%29%2C%0D%0Aline%280%2C0%2C10%2C0%29%2Cline%2813%2C8%2C10%2C0%29%2C%0D%0Aarrow%280%2C0%2C4%2C0%29%2Carrow%283%2C8%2C7%2C8%29%2C%0D%0Aarrow%280%2C0%2C1.5%2C4%29%2Carrow%2810%2C0%2C11.5%2C4%29%2C%0D%0Alocate%28-.2%2C0%2CA%29%2Clocate%282.8%2C8.8%2CB%29%2C%0D%0Alocate%289.8%2C0%2CD%29%2Clocate%2812.9%2C8.8%2CC%29%2C%0D%0Alocate%284.8%2C0%2Cb%29%2Clocate%287.8%2C8%2Cb%29%2Clocate%288.8%2C4.4%2Ch%29%2C%0D%0Aarrow%289%2C5%2C9%2C8%29%2Carrow%289%2C3%2C9%2C0%29%2C%0D%0Ared%28circle%285.8%2C6.9%2C0.1%29%29%2Cred%28arrow%283%2C8%2C5.8%2C6.9%29%29%2C%0D%0Ared%28arrow%285.8%2C6.9%2C3%2C8%29%29%2Clocate%284%2C7.5%2Cx%29%2C%0D%0Ared%28arrow%282.9%2C3.45%2C5.8%2C6.9%29%29%2Cred%28arrow%282.9%2C3.45%2C0%2C0%29%29%2C%0D%0Alocate%283.2%2C4%2C3x%29%2Clocate%285.9%2C7.3%2CE%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > because we could still calculate the areas of ADE and BCE<BR>\n" );
document.write( "based on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the length of AD and BC) as the base for both,<BR>\n" );
document.write( "and the distances from E to AB and to BC as the heights.<BR>\n" );
document.write( "And those heights would add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > anyway.<BR>\n" );
document.write( "The ratio of AE is BE, does not matter either,<BR>\n" );
document.write( "because the heights of ADE and BCE would add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > anyway. </SPAN>\n" );
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