document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=434161>Question 434161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A(0,5)B(7,1)C(-3,-2) triangle. How would i find the area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300865 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=300865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A(0,5)B(7,1)C(-3,-2) triangle. How would i find the area?<BR>\n" );
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document.write( "There are several ways to do this.<BR>\n" );
document.write( "You can find the lengths on the 3 sides, then use Heron's Law.<BR>\n" );
document.write( "Or, with the 3 sides you can find one of the altitudes, then use Area = b*h/2<BR>\n" );
document.write( "Or, find one of the angles after finding the 3 sides and use Area = the product of 2 sides x the sine of the included angle.<BR>\n" );
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document.write( "I like this method, tho.<BR>\n" );
document.write( "Make a matrix, repeating the first point<BR>\n" );
document.write( "A  B  C  A<BR>\n" );
document.write( "0  7 -3  0<BR>\n" );
document.write( "5  1 -2  5<BR>\n" );
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document.write( "Add the daigonal products starting at the upper left<BR>\n" );
document.write( "0*1 + 7*-2 + -3*5 = -29<BR>\n" );
document.write( "Do the same from the lower left<BR>\n" );
document.write( "5*7 + 1*-3 + -2*0 = 32<BR>\n" );
document.write( "The difference is 61<BR>\n" );
document.write( "The area is 61/2 = 30.5 sq units<BR>\n" );
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document.write( "This works for any polygon, with any number of sides.<BR>\n" );
document.write( "It doesn't seem to be well known.<BR>\n" );
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