document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=937864>Question 937864</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The 4-leaf figure is obtained by drawing semicircles on each side of a square with side 8. Find the area of the shaded region.\r<BR>\n" );
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document.write( "Picture for more detail: http://imgur.com/dFgevEi<BR>\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #571271 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=571271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The square has area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=8%2A8=64 ALIGN=MIDDLE  ALT=\"A=8%2A8=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( " the semi circle radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=8%2F2=4 ALIGN=MIDDLE  ALT=\"r=8%2F2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The top and bottom white region together have area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" > minus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the area of the semi circle, that is,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-2%28pi%2Ar%5E2%2F2%29 ALIGN=MIDDLE  ALT=\"8-2%28pi%2Ar%5E2%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4 ALIGN=MIDDLE  ALT=\"r=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > it will be \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-2%2A%28pi%2A4%5E2%2F2%29 ALIGN=MIDDLE  ALT=\"8-2%2A%28pi%2A4%5E2%2F2%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=8-2%2A%28pi%2A16%2F2%29 ALIGN=MIDDLE  ALT=\"8-2%2A%28pi%2A16%2F2%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=8-2%2A%288pi%29 ALIGN=MIDDLE  ALT=\"8-2%2A%288pi%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=8-16pi ALIGN=MIDDLE  ALT=\"8-16pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I will use this image because I cannot do shaded areas here:\r<BR>\n" );
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document.write( "http://imgur.com/Dpe1rJR\r<BR>\n" );
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document.write( "as you can see on a picture, radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (disregard it), our radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4 ALIGN=MIDDLE  ALT=\"r=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The area of the quarter circle is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%5E2pi%29%2F4=16pi%2F4=4pi ALIGN=MIDDLE  ALT=\"%28r%5E2pi%29%2F4=16pi%2F4=4pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "and the area of the triangle is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%294%2A4=8 ALIGN=MIDDLE  ALT=\"%281%2F2%294%2A4=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thus, the area of the half-leaf (in red) is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4pi-8 ALIGN=MIDDLE  ALT=\"4pi-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "There are two per leaf and the area of one leaf is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%284pi-8%29 ALIGN=MIDDLE  ALT=\"2%284pi-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8pi-16 ALIGN=MIDDLE  ALT=\"8pi-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "therefore the area of four leaves is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%288pi-16%29 ALIGN=MIDDLE  ALT=\"4%288pi-16%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=32%2Api-64 ALIGN=MIDDLE  ALT=\"32%2Api-64\"   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=32%2A3.14-64 ALIGN=MIDDLE  ALT=\"32%2A3.14-64\"   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=100.48-64 ALIGN=MIDDLE  ALT=\"100.48-64\"   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=36.48 ALIGN=MIDDLE  ALT=\"36.48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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