document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119330>Question 1119330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle is inside a square, with the diameter of circle equal to side of square.  .7854 is used to determine area of circle.  How is the .7854 calculated?  Non-homework. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734828 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A_square = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2 ALIGN=MIDDLE  ALT=\"s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A_circle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2+=+pi%2A%28s%2F2%29%5E2+=+pi%2As%5E2%2F4+ ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2+=+pi%2A%28s%2F2%29%5E2+=+pi%2As%5E2%2F4+\"   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=pi%2F4+ ALIGN=MIDDLE  ALT=\"pi%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 0.7854 to 4 decimal places\r<BR>\n" );
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document.write( "So A_circle = A_ square*0.7854\r<BR>\n" );
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document.write( "Dear Student:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi+ ALIGN=MIDDLE  ALT=\"pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is divided by 4 when one tries to express the area of the circle <em>in terms of the area of the square</em>:\r<BR>\n" );
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document.write( "    A_circle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2Ar%5E2+ ALIGN=MIDDLE  ALT=\"+pi%2Ar%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > —> = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2A%28s%2F2%29%5E2+ ALIGN=MIDDLE  ALT=\"+pi%2A%28s%2F2%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <<< this is A_circle in terms of the sides of the square (s). You must divide the side of the square by 2 to get the radius of the circle.  After squaring, it becomes 4 in the denominator.<br>\r<BR>\n" );
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document.write( "Continuing…   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2A%28s%5E2%2F4%29+=+%28pi%2F4%29%2As%5E2+ ALIGN=MIDDLE  ALT=\"+pi%2A%28s%5E2%2F4%29+=+%28pi%2F4%29%2As%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = approx 0.7854*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2 ALIGN=MIDDLE  ALT=\"s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.7854*A_square.\r<BR>\n" );
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document.write( "I hope you see it now.   \r<BR>\n" );
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document.write( "Note that you must somehow know the area of the square (or equivalently, the side length of the square so you can calculate the area) in order to use this formula to find the area of the circle, it simply relates the two areas.  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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