document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1115402>Question 1115402</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If A (2,5), B(-3,10) and C (-5,2) are vertices of a triangle, find its area  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #730275 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=730275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The area of a triangle with vertices (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D ALIGN=MIDDLE  ALT=\"x%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B3%5D ALIGN=MIDDLE  ALT=\"y%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28x%5B1%5D%2Ay%5B2%5D+-+x%5B2%5D%2Ay%5B1%5D+%2B+x%5B2%5D%2Ay%5B3%5D+-+x%5B3%5D%2Ay%5B2%5D+%2B+x%5B3%5D%2Ay%5B1%5D+-+x%5B1%5D%2Ay%5B3%5D%29+%2F+2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In this case, A (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >), B(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and C (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D ALIGN=MIDDLE  ALT=\"x%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B3%5D ALIGN=MIDDLE  ALT=\"y%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%282%2A10-+%28-3%29%2A5+%2B+%28-3%29%2A2+-+%28-5%29%2A10+%2B+%28-5%29%2A5+-+2%2A2%29+%2F+2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%2820%2B15+-6+%2B50+-25+-+4%29+%2F+2 ALIGN=MIDDLE  ALT=\"A+=+%2820%2B15+-6+%2B50+-25+-+4%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+50+%2F+2 ALIGN=MIDDLE  ALT=\"A+=+50+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+25 ALIGN=MIDDLE  ALT=\"A+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A similar formula can be used to find the area of any polygon. \r<BR>\n" );
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document.write( " If you prefer not to use this formula, then another method is to use Distance Formula to find the length of each side:\r<BR>\n" );
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document.write( "side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "if<BR>\n" );
document.write( "A (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "B(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "C (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"AB=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=+sqrt%282-%28-3%29%29%5E2%2B%285-10%29%5E2%29 ALIGN=MIDDLE  ALT=\"AB=+sqrt%282-%28-3%29%29%5E2%2B%285-10%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=+sqrt%282%2B3%29%5E2%2B%28-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"AB=+sqrt%282%2B3%29%5E2%2B%28-5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=sqrt%285%5E2%2B%28-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"AB=sqrt%285%5E2%2B%28-5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=sqrt%2825%2B25%29 ALIGN=MIDDLE  ALT=\"AB=sqrt%2825%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=sqrt%282%2A25%29 ALIGN=MIDDLE  ALT=\"AB=sqrt%282%2A25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=5sqrt%282%29 ALIGN=MIDDLE  ALT=\"AB=5sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=7.1+ ALIGN=MIDDLE  ALT=\"AB=7.1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"AC=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=+sqrt%282-%28-5%29%29%5E2%2B%285-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"AC=+sqrt%282-%28-5%29%29%5E2%2B%285-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=+sqrt%282%2B5%29%5E2%2B3%5E2%29 ALIGN=MIDDLE  ALT=\"AC=+sqrt%282%2B5%29%5E2%2B3%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=sqrt%287%5E2%2B3%5E2%29 ALIGN=MIDDLE  ALT=\"AC=sqrt%287%5E2%2B3%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=sqrt%2849%2B9%29 ALIGN=MIDDLE  ALT=\"AC=sqrt%2849%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=sqrt%2858%29 ALIGN=MIDDLE  ALT=\"AC=sqrt%2858%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=7.6 ALIGN=MIDDLE  ALT=\"AC=7.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"BC=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=+sqrt%28-3-%28-5%29%29%5E2%2B%2810-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"BC=+sqrt%28-3-%28-5%29%29%5E2%2B%2810-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=+sqrt%282%5E2%2B8%5E2%29 ALIGN=MIDDLE  ALT=\"BC=+sqrt%282%5E2%2B8%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=+sqrt%2868%29 ALIGN=MIDDLE  ALT=\"BC=+sqrt%2868%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=+8.25 ALIGN=MIDDLE  ALT=\"BC=+8.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since you have scalene triangle (no equal sides), you can also calculate the area from the lengths of all three sides using Heron's Formula\r<BR>\n" );
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document.write( "Calculate \"s\" (half of the triangles perimeter):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28a%2Bb%2Bc%29%2F2 ALIGN=MIDDLE  ALT=\"s+=+%28a%2Bb%2Bc%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%287.1%2B7.6%2B8.25%29%2F2 ALIGN=MIDDLE  ALT=\"s+=+%287.1%2B7.6%2B8.25%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+11.475 ALIGN=MIDDLE  ALT=\"s+=+11.475\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then calculate the Area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=sqrt%28s%28s-AB%29%28s-AC%29%28s-BC%29%29 ALIGN=MIDDLE  ALT=\"A+=sqrt%28s%28s-AB%29%28s-AC%29%28s-BC%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=sqrt%2811.475%2811.475-7.1%29%2811.475-7.6%29%2811.475-8.25%29%29 ALIGN=MIDDLE  ALT=\"A+=sqrt%2811.475%2811.475-7.1%29%2811.475-7.6%29%2811.475-8.25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=25.0476 ALIGN=MIDDLE  ALT=\"A+=25.0476\"   DISABLED_style= \"max-width:90%; height:auto;\" > round it to whole number<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=25 ALIGN=MIDDLE  ALT=\"A+=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );