document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945160>Question 945160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how i can calculate area of quadrilateral having unequal four side with known diagonal.<BR>\n" );
document.write( "Sides: 33,40,45 & 65 Diagonal:72 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576522 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=576522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would use Heron's formula to calculate the area of each of the two triangles split from the quadrilateral by the diagonal.<BR>\n" );
document.write( "Heron's formula says that the area of a triangle with sides lengths <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area=sqrt%28s%2A%28s-a%29%2A%28s-b%29%2A%28s-c%29%29 ALIGN=MIDDLE  ALT=\"area=sqrt%28s%2A%28s-a%29%2A%28s-b%29%2A%28s-c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=%28a%2Bb%2Bb%29%2F2 ALIGN=MIDDLE  ALT=\"s=%28a%2Bb%2Bb%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the \"semiperimeter\".<BR>\n" );
document.write( "I do not know what your quadrilateral looks like, or its area,<BR>\n" );
document.write( "because I do not know what side is next to the side measuring 33 and to the same side of the diagonal.<BR>\n" );
document.write( " <BR>\n" );
document.write( "IF the sides measuring 33 and 40 are to one side of the diagonal,<BR>\n" );
document.write( "and those measuring 45 and 65 are to the other side,<BR>\n" );
document.write( "the quadrilateral (with its diagonal looks like<BR>\n" );
document.write( "this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C275%2C-4%2C76%2C-45%2C10%2C%0D%0Ared%28line%280%2C0%2C72%2C0%29%29%2C%0D%0Aline%280%2C0%2C32.45%2C5.99%29%2Cline%2872%2C0%2C32.45%2C5.99%29%2C%0D%0Aline%280%2C0%2C20.72%2C-39.94%29%2Cline%2872%2C0%2C20.72%2C-39.94%29%2C%0D%0Alocate%2835%2C0%2Cred%2872%29%29%2C%0D%0Alocate%2820%2C4%2C33%29%2Clocate%2845%2C4%2C40%29%2C%0D%0Alocate%2812%2C-20%2C45%29%2Clocate%2840%2C-20%2C65%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , or this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C275%2C-4%2C76%2C-45%2C10%2C%0D%0Ared%28line%280%2C0%2C72%2C0%29%29%2C%0D%0Aline%280%2C0%2C32.45%2C5.99%29%2Cline%2872%2C0%2C32.45%2C5.99%29%2C%0D%0Aline%280%2C0%2C51.28%2C-39.94%29%2Cline%2872%2C0%2C51.28%2C-39.94%29%2C%0D%0Alocate%2835%2C0%2Cred%2872%29%29%2C%0D%0Alocate%2820%2C4%2C33%29%2Clocate%2845%2C4%2C40%29%2C%0D%0Alocate%2857%2C-20%2C45%29%2Clocate%2829%2C-20%2C65%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or maybe a flipped over version of one of those.<BR>\n" );
document.write( "The triangles' semiperimeters are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2833%2B40%2B72%29%2F2=72.5 ALIGN=MIDDLE  ALT=\"%2833%2B40%2B72%29%2F2=72.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2845%2B65%2B72%29%2F2=91 ALIGN=MIDDLE  ALT=\"%2845%2B65%2B72%29%2F2=91\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and their areas are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2872.5%2A%2872.5-33%29%2A%2872.5-40%29%2A%2872.5-72%29%29=sqrt%2872.5%2A39.5%2A32.5%2A0.5%29=215.7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded), and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2891%2A%2891-33%29%2A%2891-40%29%2A%2891-72%29%29=sqrt%2891%2A46%2A26%2A19%29=1438.0 ALIGN=MIDDLE  ALT=\"sqrt%2891%2A%2891-33%29%2A%2891-40%29%2A%2891-72%29%29=sqrt%2891%2A46%2A26%2A19%29=1438.0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( "Then, the area of the quadrilateral is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=215.7%2B1438.0=1653.7 ALIGN=MIDDLE  ALT=\"215.7%2B1438.0=1653.7\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "IF the sides measuring 33 and 45 are to one side of the diagonal,<BR>\n" );
document.write( "I calculate an area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1822.5 ALIGN=MIDDLE  ALT=\"1822.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "IF the sides measuring 33 and 65 are to one side of the diagonal,<BR>\n" );
document.write( "I calculate an area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1883.2 ALIGN=MIDDLE  ALT=\"1883.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );