document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238717>Question 238717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCD is a rectangle, and its length is twice its width. The perimeter of the rectangle is 60 units. P, Q, R, and S are the midpoints of each side. What is the area of the quadrilateral PQRS? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175428 by </B><A HREF=/tutors/aboutme.mpl?userid=JimboP1977><B>JimboP1977(311)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JimboP1977><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=JimboP1977><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The old saying that a picture says a thousand words is no more appropriate than here!\r<BR>\n" );
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document.write( "First thing to do is draw the rectangle out with the mid points.\r<BR>\n" );
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document.write( "A______P______B<BR>\n" );
document.write( "|**************|<BR>\n" );
document.write( "|**************|<BR>\n" );
document.write( "S**************Q<BR>\n" );
document.write( "|**************|             <BR>\n" );
document.write( "|**************|            <BR>\n" );
document.write( "D______R______C\r<BR>\n" );
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document.write( "Then let's put down what we know about this rectangle:\r<BR>\n" );
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document.write( "AB = 2AD  (1)<BR>\n" );
document.write( "2AB+2AD = 60  (2)\r<BR>\n" );
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document.write( "Subsituting in AB from (1) into (2) gives\r<BR>\n" );
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document.write( "2AB+AB = 60<BR>\n" );
document.write( "3AB = 60\r<BR>\n" );
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document.write( "So we know AB = 20 units\r<BR>\n" );
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document.write( "So as we know P is halfway between A and B we know that AP = 10 units\r<BR>\n" );
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document.write( "S is halfway between AD so AS must be 5 units\r<BR>\n" );
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document.write( "We know that all the corner triangles APS, BPQ, CQR, DRS are equal in size so\r<BR>\n" );
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document.write( "The total area of the rectangle ABCD minus APS, BPQ, CQR and DRS must equal the area of the remaining quadrilateral PQRS.\r<BR>\n" );
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document.write( "Area of APS = 5*10*1/2 = 25 units\r<BR>\n" );
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document.write( "So the four triangles must have an area of 4*25 = 100\r<BR>\n" );
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document.write( "Rectangles area = AB*AD = 20*10 = 200\r<BR>\n" );
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document.write( "200 - 100 = 100 units\r<BR>\n" );
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document.write( "So PQRS = 100 units.\r<BR>\n" );
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document.write( "Does this make sense? I would suggest you draw it out for youself and go through each step to make sure you understand it.\r<BR>\n" );
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document.write( "James\r<BR>\n" );
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document.write( " </SPAN>\n" );
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