document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=763263>Question 763263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of the shaded portion in the equilateral triangle with sides 6.\r<BR>\n" );
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document.write( "(assuming the central point of each arc is its corresponding \r<BR>\n" );
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document.write( "vertex)https://media.glynlyon.com/g_geo_2012/8/groupi56.gif </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464653 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=464653\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "you need to use the area of \"Sector of the circle\" formula<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28n%2F360%29r%5E2%2Api ALIGN=MIDDLE  ALT=\"A=%28n%2F360%29r%5E2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is the number of degrees in the central angle of the sector \r<BR>\n" );
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document.write( "your shaded area is equal to area of the triangle minus area of three sectors of the circle\r<BR>\n" );
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document.write( "area of the triangle:\r<BR>\n" );
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document.write( "sides length: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6 ALIGN=MIDDLE  ALT=\"c=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find 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;\" > which divides triangle into two right angle triangles whose sides are: hypotenuse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, one leg is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F2=3 ALIGN=MIDDLE  ALT=\"a%2F2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and other leg is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2=6%5E2-3%5E2 ALIGN=MIDDLE  ALT=\"h%5E2=6%5E2-3%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=h%5E2=36-9 ALIGN=MIDDLE  ALT=\"h%5E2=36-9\"   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=h%5E2=27 ALIGN=MIDDLE  ALT=\"h%5E2=27\"   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=h=sqrt%2827%29 ALIGN=MIDDLE  ALT=\"h=sqrt%2827%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=h=5.196 ALIGN=MIDDLE  ALT=\"h=5.196\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now we can find the area of triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D ALIGN=MIDDLE  ALT=\"A%5Bt%5D\"   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%5Bt%5D=%281%2F2%29a%2Ah ALIGN=MIDDLE  ALT=\"A%5Bt%5D=%281%2F2%29a%2Ah\"   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%5Bt%5D=%281%2F2%296%2A5.196 ALIGN=MIDDLE  ALT=\"A%5Bt%5D=%281%2F2%296%2A5.196\"   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%5Bt%5D=3%2A5.196 ALIGN=MIDDLE  ALT=\"A%5Bt%5D=3%2A5.196\"   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%5Bt%5D=15.588 ALIGN=MIDDLE  ALT=\"A%5Bt%5D=15.588\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find area of circle sector:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bcs%5D=%28n%2F360%29r%5E2%2Api ALIGN=MIDDLE  ALT=\"A%5Bcs%5D=%28n%2F360%29r%5E2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=60 ALIGN=MIDDLE  ALT=\"n=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3 ALIGN=MIDDLE  ALT=\"r=3\"   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%5Bcs%5D=%2860%2F360%293%5E2%2A3.14 ALIGN=MIDDLE  ALT=\"A%5Bcs%5D=%2860%2F360%293%5E2%2A3.14\"   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%5Bcs%5D=%281%2F6%299%2A3.14 ALIGN=MIDDLE  ALT=\"A%5Bcs%5D=%281%2F6%299%2A3.14\"   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%5Bcs%5D=28.26%2F6 ALIGN=MIDDLE  ALT=\"A%5Bcs%5D=28.26%2F6\"   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%5Bcs%5D=4.71 ALIGN=MIDDLE  ALT=\"A%5Bcs%5D=4.71\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you have three of these sectors, so total area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3A%5Bcs%5D=3%2A4.71 ALIGN=MIDDLE  ALT=\"3A%5Bcs%5D=3%2A4.71\"   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=3A%5Bcs%5D=14.13 ALIGN=MIDDLE  ALT=\"3A%5Bcs%5D=14.13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now we can find the area of the shaded portion: it is equal to difference between the area of the triangle and three sectors\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bshaded_portion%5D=A%5Bt%5D-3A%5Bcs%5D=15.588-14.13 ALIGN=MIDDLE  ALT=\"A%5Bshaded_portion%5D=A%5Bt%5D-3A%5Bcs%5D=15.588-14.13\"   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%5Bshaded_portion%5D=A%5Bt%5D-3A%5Bcs%5D=1.458 ALIGN=MIDDLE  ALT=\"A%5Bshaded_portion%5D=A%5Bt%5D-3A%5Bcs%5D=1.458\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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