document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54895>Question 54895</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0130413968/algebrahomeworkh>Roads to Geometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The question in the text is: The area of a trapezoid is the product of its height and the arithmetic mean of its bases.\r<BR>\n" );
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document.write( "I know what the answer would be, a general formula. I just dont know how to go about getting a written proof for the problem.\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37152 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=37152\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> construct a rectangle by dropping perpendiculars from one parallel side to<BR>\n" );
document.write( "the other parallel side. Call the height of the perpendiculars h.<BR>\n" );
document.write( "Call the other side l, which is the length of the shortest parallel side.<BR>\n" );
document.write( "h*l is the area of this rectangle.<BR>\n" );
document.write( "Now you have to find lthe areas of the two triangles that are left.<BR>\n" );
document.write( "Call the bases of the triangles x and y. Their heights are both h.<BR>\n" );
document.write( "Their areas are<BR>\n" );
document.write( "(1/2)*x*h and<BR>\n" );
document.write( "(1/2)*y*h<BR>\n" );
document.write( "Now add the 3 areas<BR>\n" );
document.write( "A = h*l + (1/2)*x*h + (1/2)*y*h<BR>\n" );
document.write( "Multiply the 1st term by 2/2. This is OK since 2/2 = 1<BR>\n" );
document.write( "A = (2/2)*h*l + (1/2)*x*h + (1/2)*y*h<BR>\n" );
document.write( "factor out (1/2)*h<BR>\n" );
document.write( "A = (1/2)*h*(2l + x + y)<BR>\n" );
document.write( "or, what is the same thing,<BR>\n" );
document.write( "A = h*((2l + x + y)/2)<BR>\n" );
document.write( "This is what is required. (2l + x + y) can be written (l + x + y + l}<BR>\n" );
document.write( "l is one side and x + y + l is the other side   </SPAN>\n" );
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