document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128341>Question 128341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circular pond will be placed on a square piece of land.The length of a side of the square is 2x.The radius of the pond is x.The part of the square not covered by the pond will be planted with flowers.What's the area of the region that will be planted with flowers?Write your answer in factored form. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93976 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Although it is not necessary to do so in solving this problem, try to envision a picture of<BR>\n" );
document.write( "what the pond and the square area look like. The circular pond has a diameter of twice its<BR>\n" );
document.write( "radius, and since the radius is x, the diameter of the circle is 2x. But the length of the<BR>\n" );
document.write( "side of the square is also 2x. Therefore, the circle is inscribed in the square such that<BR>\n" );
document.write( "the circle will touch all four sides of the square. The center of the circle will be exactly<BR>\n" );
document.write( "at the point where the two diagonals of the square cross.<BR>\n" );
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document.write( "What you are trying to find is the total area of the four regions that lie outside the circle<BR>\n" );
document.write( "but inside the square. <BR>\n" );
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document.write( "To do that, just find the area of the square and from that area subtract the area of the<BR>\n" );
document.write( "circle. The difference will be the total area of the four odd-shaped pieces.<BR>\n" );
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document.write( "The area of the square is found by multiplying two of its sides. This area is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+2x%2A2x+=+4x%5E2 ALIGN=MIDDLE  ALT=\"A+=+2x%2A2x+=+4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And the area of the circular pond is found by squaring its radius and multiplying that<BR>\n" );
document.write( "result by pi. For this problem that area is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+pi%2Ax%5E2 ALIGN=MIDDLE  ALT=\"A+=+pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The total area of the four odd shaped pieces is the area of the garden and is equal to<BR>\n" );
document.write( "the differences of the two areas we found above. The garden area is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+4x%5E2+-+pi%2Ax%5E2 ALIGN=MIDDLE  ALT=\"A+=+4x%5E2+-+pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And if you prefer, you can factor the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to write the garden area as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+x%5E2%2A%284+-+pi%29 ALIGN=MIDDLE  ALT=\"A+=+x%5E2%2A%284+-+pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to solve it.<BR>\n" );
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document.write( " </SPAN>\n" );
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