document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149554>Question 1149554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the area of the rectangle? Show all work.\r<BR>\n" );
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document.write( "Coordinates: (-4, 0), (-6, 4), (4, 4), (2, 8)\r<BR>\n" );
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document.write( "Do not round anything until the very end.<BR>\n" );
document.write( "Round your final answer to the tenths place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770888 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=770888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the area of the rectangle? Show all work.\r<BR>\n" );
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document.write( "Coordinates: A(-4, 0), B(-6, 4), C(4, 4), D(2, 8)<BR>\n" );
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document.write( "Here's a method for any polygon, and # of sides:<BR>\n" );
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document.write( " A    B    C    D    A\r\n" );
document.write( "-4   -6    4    2   -4\r\n" );
document.write( " 0    4    4    8    0\r\n" );
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document.write( "Add the diagonal products starting at the upper left:<BR>\n" );
document.write( "-4*4 + -6*4 + 4*8 + 2*0 = -16 - 24 + 32 + 0 = 8<BR>\n" );
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document.write( "Add the diagonal products starting at the lower left:<BR>\n" );
document.write( "0*-6 + 4*4 + 4*2 + 8*-4 = 16 + 8 -32 = -8<BR>\n" );
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document.write( "The difference is 16<BR>\n" );
document.write( "The area is 1/2 that, = 8 sq units.<BR>\n" );
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document.write( "The points have to be in order around the polygon, the only restriction.<BR>\n" );
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document.write( "The points are not in order, so the area is not 8 sq units.<BR>\n" );
document.write( "You can list them in order, then do the calculations.<BR>\n" );
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document.write( "It seems to work for polygons of all shapes, not just convex polygons, but I'm not yet certain of that.<BR>\n" );
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document.write( "Update:  it works for all \"simple polygons.\"  Which means the vertices are listed in order.<BR>\n" );
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document.write( "Ref:  CRC Press, 32nd Edition\r<BR>\n" );
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