document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099501>Question 1099501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In parallelogram ABCD, line EF is perpendicular to line AB and line GH is perpendicular to BD. Compute the area of the parallelogram, given AD=22, AE=13, EF=12, BG=17, and GH=8. \r<BR>\n" );
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document.write( "link for the problem https://gyazo.com/fc882226a5f618fc9931d6a27147f4ac </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713933 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=713933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C140%2C-2%2C28%2C-2%2C12%2C%0D%0Atriangle%280%2C0%2C22%2C0%2C4%2C9.6%29%2C%0D%0Atriangle%2822%2C0%2C26%2C9.6%2C4%2C9.6%29%2C%0D%0Atriangle%280%2C0%2C13%2C0%2C1.923%2C4.615%29%2C%0D%0Atriangle%284%2C9.6%2C21%2C9.6%2C17.235%2C2.541%29%2C%0D%0Alocate%28-0.5%2C0%2CA%29%2Clocate%2821.5%2C0%2CD%29%2C%0D%0Alocate%283.7%2C11%2CB%29%2Clocate%2825.8%2C11%2CC%29%2C%0D%0Alocate%2812.5%2C0%2CE%29%2Clocate%281.4%2C5.9%2CF%29%2C%0D%0Alocate%2820.8%2C11%2CG%29%2Clocate%2816.8%2C2.6%2CH%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Right triangle AEF, with a right angle at F,<BR>\n" );
document.write( "has hypotenuse AE=13, leg EF=12, and leg AF that we can calculate as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AF=sqrt%2813%5E2-12%5E2%29=sqrt%2825%29=5 ALIGN=MIDDLE  ALT=\"AF=sqrt%2813%5E2-12%5E2%29=sqrt%2825%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Right triangle BGH, with a right angle at H,<BR>\n" );
document.write( "has hypotenuse BG=17, leg GH=8, and leg BH that we can calculate as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BH=sqrt%2817%5E2-8%5E2%29=sqrt%28225%29=15 ALIGN=MIDDLE  ALT=\"BH=sqrt%2817%5E2-8%5E2%29=sqrt%28225%29=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "From those two triangles,we could get angles BAD and ADB=DBC,<BR>\n" );
document.write( "and with AD=22, we would have angle-side-angle of triangle ABD,<BR>\n" );
document.write( "which is half of the parallelogram.<BR>\n" );
document.write( "That looks complicated, though.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If we find the height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, perpendicular to AD, we could calculate the area as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2AAD ALIGN=MIDDLE  ALT=\"h%2AAD\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C140%2C-2%2C28%2C-2%2C12%2C%0D%0Agreen%28triangle%280%2C0%2C4%2C0%2C4%2C9.6%29%29%2C%0D%0Agreen%28rectangle%284%2C0%2C3.5%2C0.5%29%29%2C%0D%0Atriangle%280%2C0%2C22%2C0%2C4%2C9.6%29%2C%0D%0Atriangle%2822%2C0%2C26%2C9.6%2C4%2C9.6%29%2C%0D%0Atriangle%280%2C0%2C13%2C0%2C1.923%2C4.615%29%2C%0D%0Atriangle%284%2C9.6%2C21%2C9.6%2C17.235%2C2.541%29%2C%0D%0Alocate%28-0.5%2C0%2CA%29%2Clocate%2821.5%2C0%2CD%29%2C%0D%0Alocate%283.7%2C11%2CB%29%2Clocate%2825.8%2C11%2CC%29%2C%0D%0Alocate%2812.5%2C0%2CE%29%2Clocate%281.4%2C5.9%2CF%29%2C%0D%0Alocate%2820.8%2C11%2CG%29%2Clocate%2816.8%2C2.6%2CH%29%2C%0D%0Alocate%284.2%2C5.9%2Cgreen%28h%29%29%2Clocate%283.7%2C0%2CI%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The height drawn forms right triangle ABI,<BR>\n" );
document.write( "and right triangle BDI.<BR>\n" );
document.write( "ABI shares the angle at A angle with right triangle AEF,<BR>\n" );
document.write( "so they are similar right triangles.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AI%2FBI=AF%2FEF=5%2F12 ALIGN=MIDDLE  ALT=\"AI%2FBI=AF%2FEF=5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "BDI has angle BDI, congruent with angle GBH,<BR>\n" );
document.write( "and that makes right triangles BDI similar to right triangle GBH.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ID%2FBI=BH%2FGH=15%2F8 ALIGN=MIDDLE  ALT=\"ID%2FBI=BH%2FGH=15%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AI%2FBI=5%2F12 ALIGN=MIDDLE  ALT=\"AI%2FBI=5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ID%2FBI=15%2F8 ALIGN=MIDDLE  ALT=\"ID%2FBI=15%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AI%2FBI%2BID%2FBI=5%2F12%2B15%2F8 ALIGN=MIDDLE  ALT=\"AI%2FBI%2BID%2FBI=5%2F12%2B15%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AI%2BID%29%2FBI=55%2F24 ALIGN=MIDDLE  ALT=\"%28AI%2BID%29%2FBI=55%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD%2FBI=55%2F24 ALIGN=MIDDLE  ALT=\"AD%2FBI=55%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2FBI=55%2F24 ALIGN=MIDDLE  ALT=\"22%2FBI=55%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BI%2A55=22%2A24 ALIGN=MIDDLE  ALT=\"BI%2A55=22%2A24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BI=22%2A24%2F55=9.6 ALIGN=MIDDLE  ALT=\"BI=22%2A24%2F55=9.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As BI-9.6 is the height of the parallelogram relative to base AD=22,<BR>\n" );
document.write( "the area of the parallelogram is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BI%2AAD=9.6%2A22=highlight%28211.2%29 ALIGN=MIDDLE  ALT=\"BI%2AAD=9.6%2A22=highlight%28211.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );