document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148964>Question 1148964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCD is a trapezoid in which AD:BC = 2:5. If the area of triangle AMD is 624cm2, find the area of the trapezoid in cm2.<BR>\n" );
document.write( "Diagram: https://imgur.com/a/kqz5EdC\r<BR>\n" );
document.write( "\n" );
document.write( "Happy Saturday tutors! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770305 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=770305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Triangles AMD and CMB are similar.  Since the bases are in the ratio 2:5, their heights are in the ratio 2:5, and their areas are in the ratio 2^2:5^2 = 4:25.<br><BR>\n" );
document.write( "So, given that the area of AMD is 624, we know the area of CMB is 624*(25/4) = 3900.<br><BR>\n" );
document.write( "Triangles AMD and ABD share base AD; and the ratio of their altitudes is 2:(2+5) = 2:7.  So the area of triangle ABD is 624*(7/2) = 2184; and then the area of triangle ABM is 2184-624 = 1560.<br><BR>\n" );
document.write( "By a similar argument, the area of triangle DMC is also 1560.<br><BR>\n" );
document.write( "So the area of the trapezoid is<br><BR>\n" );
document.write( "624+3900+2(1560) = 7644 cm^2.<br><BR>\n" );
document.write( "------------------------------------------------------------<br><BR>\n" );
document.write( "Added in response to the reader's question....<br><BR>\n" );
document.write( "The ratio of similarity between triangles AMD and CMB is 2:5, not 2:7.<br><BR>\n" );
document.write( "2:7 is the ratio of the height of triangle AMD to the height of the trapezoid.<br><BR>\n" );
document.write( "2:7 is also the ratio between the heights of triangles AMD and ABD; and between the heights of triangles AMD and DMC.<br>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );