document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190624>Question 190624</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Estimate the area of the rectangle in square units. Each square represents 1 square unit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143097 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=143097\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, I'm going to categorize the portions of the rectangle. The red portions are grid squares that are completely enclosed by the rectangle, the green portions are the corners and finally the blue regions are the edges. \r<BR>\n" );
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document.write( "Note: image is not to scale\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/work/rectangle1.png\">\r<BR>\n" );
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document.write( "Let's find the area of the red region:\r<BR>\n" );
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document.write( "Notice how there are 3 red squares in the middle. So the area of these three red squares is: 3*1=3 (since each square is one square unit). So this means that the area of the rectangle is at least 3 square units\r<BR>\n" );
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document.write( "Now let's find the area of the blue region:\r<BR>\n" );
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document.write( "First, let's estimate the area of one of the blue regions that lies on top of the rectangle. One of these regions is 1 unit across and about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units high (just a guess). So the area of one blue tile is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%283%2F4%29=3%2F4 ALIGN=MIDDLE  ALT=\"1%283%2F4%29=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > square units. \r<BR>\n" );
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document.write( "Now multiply this single area by 6 (since there are 6 blue tiles that line the top and bottom) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29%286%29=18%2F4=9%2F2=4.5 ALIGN=MIDDLE  ALT=\"%283%2F4%29%286%29=18%2F4=9%2F2=4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the total area of the blue tiles that line the top and bottom is about 4.5 square units\r<BR>\n" );
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document.write( "Now let's estimate the area of the blue tiles that line the sides. The height is 1 unit and the width is about half, so the area is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%281%2F2%29=1%2F2 ALIGN=MIDDLE  ALT=\"1%281%2F2%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Double this value (there are two blue tiles on the side) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%281%2F2%29=1 ALIGN=MIDDLE  ALT=\"2%281%2F2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the area of the lateral blue tiles is about 1 square unit\r<BR>\n" );
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document.write( "Add this to the area of the tiles that line the top/bottom to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B4.5=5.5 ALIGN=MIDDLE  ALT=\"1%2B4.5=5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the total area of the blue tiles is about 5.5 square units.\r<BR>\n" );
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document.write( "Finally, let's find the area of the green region:\r<BR>\n" );
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document.write( "Looking at one green tile, each tile is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > units wide and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long. So this means that the area of one green tile is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%283%2F4%29=%281%2A3%29%2F%282%2A4%29=3%2F8 ALIGN=MIDDLE  ALT=\"%281%2F2%29%283%2F4%29=%281%2A3%29%2F%282%2A4%29=3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > square units\r<BR>\n" );
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document.write( "Multiply this area by 4 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%283%2F8%29=12%2F8=3%2F2=1.5 ALIGN=MIDDLE  ALT=\"4%283%2F8%29=12%2F8=3%2F2=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the total area of the green region is about 1.5 square units\r<BR>\n" );
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document.write( "Now add up the three separate areas to get\r<BR>\n" );
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document.write( "Area of Red + Area of Blue + Area of Green = 3 + 5.5 + 1.5 = 10\r<BR>\n" );
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document.write( "So the total estimated area of the rectangle is about 10 square units. </SPAN>\n" );
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