document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199005>Question 1199005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The figure below is a trapezium in which AB=40 cm, BC=25 cm, CD=12 cm and AD=17 cm. Calculate the  area of the trapezium.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832685 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=832685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here is a sketch, showing altitudes DE and CF:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C200%2C0%2C50%2C0%2C20%0D%0A%2Cline%282%2C2%2C42%2C2%29%2Cline%282%2C2%2C10%2C17%29%2Cline%2810%2C17%2C22%2C17%29%2Cline%2822%2C17%2C42%2C2%29%0D%0A%2Cline%2810%2C2%2C10%2C17%29%2Cline%2822%2C2%2C22%2C17%29%0D%0A%2Clocate%281%2C2%2CA%29%2Clocate%2842%2C2%2CB%29%2Clocate%2822%2C19%2CC%29%2Clocate%289%2C19%2CD%29%2Clocate%289%2C2%2CE%29%2Clocate%2821%2C2%2CF%29%0D%0A%2Clocate%284%2C12%2C17%29%2Clocate%2816%2C19%2C12%29%2Clocate%2832%2C12%2C25%29%2Clocate%2811%2C9%2Ch%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The quick path to the answer is to guess that all the numbers in the problem are whole numbers.  So look for Pythagorean triples.  With AD=17, it is likely that AE is 8 and the altitude h is 15; and with the altitude 15, FB would be 20.  And 8+12+20 = 40, as required.<br><BR>\n" );
document.write( "So the bases are 12 and 40, and the height is 15; the area is 15*((12+40)/2) = 15*26 = 390.<br><BR>\n" );
document.write( "ANSWER: 390<br><BR>\n" );
document.write( "If you want a formal algebraic solution....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AE+=+sqrt%2817%5E2-h%5E2%29 ALIGN=MIDDLE  ALT=\"AE+=+sqrt%2817%5E2-h%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FB+=+sqrt%2825%5E2-h%5E2%29 ALIGN=MIDDLE  ALT=\"FB+=+sqrt%2825%5E2-h%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2817%5E2-h%5E2%29%2B12%2Bsqrt%2825%5E2-h%5E2%29=40 ALIGN=MIDDLE  ALT=\"sqrt%2817%5E2-h%5E2%29%2B12%2Bsqrt%2825%5E2-h%5E2%29=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I won't go through the whole process of solving that equation....<br><BR>\n" );
document.write( "To solve it, isolate one of the square roots on one side of the equation and square both sides.  That will leave you still with one square root; again isolate it and square both sides.  Now you will have no square roots left; and the remaining equation can be solved for the altitude h with only mildly ugly arithmetic.<br><BR>\n" );
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