document.write( "Question 1191686: A rounded metal plate is made from a rectangular sheet of metal of size x cms by y cms. Each corner is rounded off to a quadrant of circle, radius r.\r
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Algebra.Com's Answer #823481 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "We start with a rectangle which has area \r\n" );
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document.write( "Then we round off the corners, which means that we\r\n" );
document.write( "subtract the 4 little corners that we round off from\r\n" );
document.write( "the original area which is .\r\n" );
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document.write( "Next we draw in the quadrants of a circle of radius r to help us\r\n" );
document.write( "see how much was subtracted from the corners in the rounding \r\n" );
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document.write( "Now we look at just those quadrants of a circle:\r\n" );
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document.write( "Now we put the four together and have a circle inscribed in a square\r\n" );
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document.write( "Now we can see how much we have to subtract off from the\r\n" );
document.write( "area of the original rectangle whose area is \r\n" );
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document.write( "We have the area of a square whose side is twice the radius r.\r\n" );
document.write( "That's .  From that we subtract the area of the\r\n" );
document.write( "circle , and get .\r\n" );
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document.write( "That means the area of the rounded metal plate is xy minus\r\n" );
document.write( "the area of those corners.\r\n" );
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document.write( "We can factor out the r² in the last two terms:\r\n" );
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document.write( "  <--expression for A\r\n" );
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document.write( "To get your answer for r, go back to the previous step:\r\n" );
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document.write( "Edwin

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