document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187826>Question 1187826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> https://imgur.com/8J0Mleu ABCD is a trapezoid with AD ||BC. If AD = 5 cm and BC = 11 cm, and if the area of the trapezoid is 80 cm^2, find the area of triangle ABE, in cm^2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818833 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" > parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E ALIGN=MIDDLE  ALT=\"E\"   DISABLED_style= \"max-width:90%; height:auto;\" > the midpoint of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD ALIGN=MIDDLE  ALT=\"CD\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the area of triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABE ALIGN=MIDDLE  ALT=\"ABE\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=half ALIGN=MIDDLE  ALT=\"half\"   DISABLED_style= \"max-width:90%; height:auto;\" > the area of the trapezoid.\r<BR>\n" );
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document.write( "ANSWER: The area of triangle ABE is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=166cm%5E2%2F2+=+83cm%5E2 ALIGN=MIDDLE  ALT=\"166cm%5E2%2F2+=+83cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "To see that this is true, consider the midline <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EF ALIGN=MIDDLE  ALT=\"EF\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the trapezoid.\r<BR>\n" );
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document.write( "Let the height of the trapezoid be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >; then the altitudes of triangles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ADE ALIGN=MIDDLE  ALT=\"ADE\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AFE ALIGN=MIDDLE  ALT=\"+AFE\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BFE ALIGN=MIDDLE  ALT=\"BFE\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BEC ALIGN=MIDDLE  ALT=\"BEC\"   DISABLED_style= \"max-width:90%; height:auto;\" > are all<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x ALIGN=MIDDLE  ALT=\"+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The area of triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABE ALIGN=MIDDLE  ALT=\"ABE\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the sum of the areas of triangles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AFE ALIGN=MIDDLE  ALT=\"AFE\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BFE ALIGN=MIDDLE  ALT=\"BFE\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2811%29%28x%29%2B%281%2F2%29%2811%29%28x%29+=+11x ALIGN=MIDDLE  ALT=\"%281%2F2%29%2811%29%28x%29%2B%281%2F2%29%2811%29%28x%29+=+11x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The area of the trapezoid is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%288%2B14%29%282x%29+=+22x ALIGN=MIDDLE  ALT=\"%281%2F2%29%288%2B14%29%282x%29+=+22x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the area of triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABE ALIGN=MIDDLE  ALT=\"ABE\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=half+ ALIGN=MIDDLE  ALT=\"half+\"   DISABLED_style= \"max-width:90%; height:auto;\" >the area of the trapezoid.\r<BR>\n" );
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