document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204418>Question 1204418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of the parallelogram with the following vertices:\r<BR>\n" );
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document.write( "1. (-2, 3), (5, 8), (3, 3), and (0, 8)\r<BR>\n" );
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document.write( "A. 16 sq units<BR>\n" );
document.write( "B. 20 sq units<BR>\n" );
document.write( "C. 34 sq units<BR>\n" );
document.write( "D. 18 sq units<BR>\n" );
document.write( "E. 25 sq units<BR>\n" );
document.write( "F. 36 sq units\r<BR>\n" );
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document.write( "2. (-2, 7), (-4, 4), (-11, 4), and (-9, 7)\r<BR>\n" );
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document.write( "A. 15 sq units<BR>\n" );
document.write( "B. 63 sq units<BR>\n" );
document.write( "C. 28 sq units<BR>\n" );
document.write( "D. 21 sq units<BR>\n" );
document.write( "E. 36 sq units<BR>\n" );
document.write( "F. 14 sq units\r<BR>\n" );
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document.write( "3. (-6, 6), (-6, 3), (-12, 3), and (-12, 6)\r<BR>\n" );
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document.write( "A. 36 sq units<BR>\n" );
document.write( "B. 54 sq units<BR>\n" );
document.write( "C. 15 sq units<BR>\n" );
document.write( "D. -45 sq units<BR>\n" );
document.write( "E. 18 sq units<BR>\n" );
document.write( "F. 24 sq units\r<BR>\n" );
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document.write( "4. (12, -3), (5, -6), (5, -3), and (12, -6)\r<BR>\n" );
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document.write( "A. 21 sq units<BR>\n" );
document.write( "B. -17 sq units<BR>\n" );
document.write( "C. 50 sq units<BR>\n" );
document.write( "D. 32.5 sq units<BR>\n" );
document.write( "E. 42 sq units<BR>\n" );
document.write( "F. 30 sq units´\r<BR>\n" );
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document.write( "5. (-2, 2), (-6, 9), (-13, 9), and (-9, 2)\r<BR>\n" );
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document.write( "A. 10 sq units<BR>\n" );
document.write( "B. 25 sq units<BR>\n" );
document.write( "C. -55 sq units<BR>\n" );
document.write( "D. 64 sq units<BR>\n" );
document.write( "E. 35 sq units<BR>\n" );
document.write( "F. 49 sq units </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840645 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=840645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor says to use a magical formula for the area of a parallelogram in terms of the coordinates of the vertices.<br><BR>\n" );
document.write( "That is a good method if all you want to do is to get the answers without learning anything.<br><BR>\n" );
document.write( "In every one of these examples, one pair of sides is either horizontal or vertical, so you can find the area in each case using the basic formula,<br><BR>\n" );
document.write( "Area = base * height<br><BR>\n" );
document.write( "I will get you started on a couple of your examples.<br><BR>\n" );
document.write( "2. (-2, 7), (-4, 4), (-11, 4), and (-9, 7)<br><BR>\n" );
document.write( "(-2,7) and (-9,7) determine a horizontal segment of length 7; (-4,4) and (-11,4) determine another horizontal segment of length 7.  The vertical distance between those two horizontal segments is the difference between 4 and 7, which is 3.  So the area is 7*3 = 21.<br><BR>\n" );
document.write( "3. (-6, 6), (-6, 3), (-12, 3), and (-12, 6)<br><BR>\n" );
document.write( "(-6,6) and (-6,3) determine a vertical segment of length 3; (-12,3) and (-12,6) determine another vertical segment of length 3.  The horizontal distance between those two vertical segments is the difference between -6 and -12, which is -6.  So the area is 3*6 = 18.  Note that this parallelogram is in fact a rectangle.<br><BR>\n" );
document.write( "Work the other examples by the same process.<br><BR>\n" );
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