document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148863>Question 1148863</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the diagram AD=5cm, EF=2cm, and parallel segments are indicated. If the total area of the trapezoid is 68cm2, what is the area, in cm2, of triangle AMN\r<BR>\n" );
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document.write( "Diagram: https://imgur.com/a/JhZZ9W0 </SPAN>\n" );
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document.write( "Cool problem.  Solve by determining the height of the trapezoid from the given information and then looking at some similar triangles....<br><BR>\n" );
document.write( "Given: AD=5, EF=2; area of ABCD is 68.<br><BR>\n" );
document.write( "BE=5 because ABED is a parallelogram; FC=5 because AFCD is a parallelogram.<br><BR>\n" );
document.write( "BC=5+2+5 = 12.<br><BR>\n" );
document.write( "Area of ABCD = 68 = (1/2)(5+12)(h)  -->  the height of the trapezoid is 8.<br><BR>\n" );
document.write( "Triangles AND and FNE are similar, in the ratio 5:2.  In particular, the heights of those two triangles (measured perpendicular to the bases of the trapezoid) are in the ratio 5:2.  Since the height of the trapezoid is 8, the height of triangle AND is (5/7)*8 = 40/7.<br><BR>\n" );
document.write( "Triangles ADM and CME are similar, in the ratio 5:7.  In particular, the heights of those two triangles (measured perpendicular to the bases of the trapezoid) are in the ratio 5:7.  Since the height of the trapezoid is 8, the height of triangle ADM is (5/12)*8 = 40/12 = 10/3.<br><BR>\n" );
document.write( "The area of triangle AMN is the difference between the areas of triangles AND and AMD:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%285%29%2840%2F7-10%2F3%29+=+%285%2F2%29%28%28120-70%29%2F21%29+=+125%2F21 ALIGN=MIDDLE  ALT=\"%281%2F2%29%285%29%2840%2F7-10%2F3%29+=+%285%2F2%29%28%28120-70%29%2F21%29+=+125%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The area of triangle AMN is 125/21 cm^2.<br><BR>\n" );
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