document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110368>Question 1110368</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCD is a trapezoid. E is a point between B and C. 2|BE| = |EC|, 5|AB| = 3|DC|<BR>\n" );
document.write( "Area of DEC is 10. So what is area of AED? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725366 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=725366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><font size=\"4\" color=red>The answer is 11</font>\r<BR>\n" );
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document.write( "See the steps below to see how I got that answer\r<BR>\n" );
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document.write( "A diagram isn't 100% mandatory, but for me it really helps.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/6rXj6hp.png\"><BR>\n" );
document.write( "Based on the diagram we have...<BR>\n" );
document.write( "x = vertical distance from point C to point E<BR>\n" );
document.write( "y = vertical distance from point E to point B<BR>\n" );
document.write( "z = |AB| = distance from A to B<BR>\n" );
document.write( "w = |DC| = distance from C to D<BR>\n" );
document.write( "T1 = area of the gray triangle ABE<BR>\n" );
document.write( "T2 = area of the green triangle AED<BR>\n" );
document.write( "T3 = area of the red triangle DEC\r<BR>\n" );
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document.write( "Because 2|BE| = |EC| and because E is on segment BC, this means that the vertical component from C to E is twice that as the vertical component from E to B. <BR>\n" );
document.write( "In other words, x = 2y\r<BR>\n" );
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document.write( "Also,<BR>\n" );
document.write( "5|AB| = 3|DC|<BR>\n" );
document.write( "5*z = 3*w<BR>\n" );
document.write( "w = 5z/3\r<BR>\n" );
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document.write( "We will use the two equations x = 2y and w = 5z/3 for the sections below<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "T3 = area of triangle DEC (red triangle)<BR>\n" );
document.write( "T3 = (base*height)/2<BR>\n" );
document.write( "T3 = x*w/2<BR>\n" );
document.write( "10 = x*w/2 .... plug in the given area for triangle DEC (which was 10 square units)<BR>\n" );
document.write( "2*10 = x*w<BR>\n" );
document.write( "20 = x*w<BR>\n" );
document.write( "20 = (2y)*(5z/3) .... plug in x = 2y; plug in w = 5z/3<BR>\n" );
document.write( "20 = 10yz/3<BR>\n" );
document.write( "3*20 = 10yz<BR>\n" );
document.write( "60 = 10yz<BR>\n" );
document.write( "6 = yz<BR>\n" );
document.write( "yz = 6 ... this will be used later<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "A = area of trapezoid<BR>\n" );
document.write( "A = height*(base1+base2)/2<BR>\n" );
document.write( "A = h*(b1+b2)/2<BR>\n" );
document.write( "A = (x+y)*(w+z)/2<BR>\n" );
document.write( "A = (2y+y)*(w+z)/2 .... plug in x = 2y<BR>\n" );
document.write( "A = 3y*(w+z)/2<BR>\n" );
document.write( "A = 3y*(5z/3+z)/2 .... plug in w = 5z/3<BR>\n" );
document.write( "A = 3y*(5z/3+3z/3)/2<BR>\n" );
document.write( "A = 3y*(8z/3)/2<BR>\n" );
document.write( "A = 3y*8z/6<BR>\n" );
document.write( "A = 3y*4z/3<BR>\n" );
document.write( "A = 12yz/3<BR>\n" );
document.write( "A = 4yz<BR>\n" );
document.write( "A = 4*6 .... replace yz with 6 (since it was found earlier that yz = 6)<BR>\n" );
document.write( "A = 24<BR>\n" );
document.write( "The area of the trapezoid is 24 square units<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "T1 = area of gray triangle ABE<BR>\n" );
document.write( "T1 = (base*height)/2<BR>\n" );
document.write( "T1 = z*y/2<BR>\n" );
document.write( "T1 = yz/2<BR>\n" );
document.write( "T1 = 6/2 .... replace yz with 6<BR>\n" );
document.write( "T1 = 3<BR>\n" );
document.write( "The gray triangle T1 has area 3 square units<BR>\n" );
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document.write( "T2 = area of green triangle AED (what we want)<BR>\n" );
document.write( "T2 = A - T1 - T3<BR>\n" );
document.write( "T2 = 24 - 3 - 10<BR>\n" );
document.write( "T2 = 11\r<BR>\n" );
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document.write( "So that's why <font size=\"4\" color=red>the answer is 11</font><BR>\n" );
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