document.write( "Question 753612: The area of a square is 72 cm. The area of the circle drawn on its diagonal is?\r
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Algebra.Com's Answer #458500 by Edwin McCravy(20060)\"\" \"About 
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The area of a square is 72 cm. The area of the circle drawn on its diagonal is?
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document.write( "I can't tell what is meant by \"the circle drawn on its diagonal\".\r\n" );
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document.write( "THIS:OR THIS:\r\n" );
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document.write( "In either case we calculate s the length of a side of the square, \r\n" );
document.write( "using:\r\n" );
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document.write( "    A = s²\r\n" );
document.write( "   72 = s²\r\n" );
document.write( "  √72 = √s²\r\n" );
document.write( "  √72 = s\r\n" );
document.write( "√36·2 = s\r\n" );
document.write( "  6√2 = s\r\n" );
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document.write( "If it's the first case we draw a horizontal diameter (in green) which is equal\r\n" );
document.write( "in length to the side of the square, 6√2. and therefore each radius is half of \r\n" );
document.write( "that or 3√2\r\n" );
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document.write( "So to find the area of the circle we use:\r\n" );
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document.write( "A = pr2\r\n" );
document.write( "A = p(3√2)2\r\n" );
document.write( "A = p·32·(√2)2\r\n" );
document.write( "A = p·9·2\r\n" );
document.write( "A = 18p cm²\r\n" );
document.write( "A ≈ 56.55 cm² \r\n" );
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document.write( "But if it's the second way, then the diagonal is the diameter\r\n" );
document.write( "of the circle, d:\r\n" );
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document.write( "We calculate d with the Pythagorean theorem:\r\n" );
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document.write( "d2 = (6√2)2 + (6√2)2\r\n" );
document.write( "d2 = 2·(6√2)2 \r\n" );
document.write( "d2 = 2·62(√2)2\r\n" );
document.write( "d2 = 2·36·2\r\n" );
document.write( "d2 = 144\r\n" );
document.write( " d = 12\r\n" );
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document.write( "And the radius is half the diameter, so the radius of the circle\r\n" );
document.write( "is 6 cm.\r\n" );
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document.write( "To find the area of the circle we use:\r\n" );
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document.write( "A = pr2\r\n" );
document.write( "A = p62\r\n" );
document.write( "A = p·36\r\n" );
document.write( "A = 36p cm²\r\n" );
document.write( "A ≈ 113.1 cm²\r\n" );
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document.write( "The area of the circle in the second case is exactly twice\r\n" );
document.write( "the area in the first case.  That is to say, the circle\r\n" );
document.write( "circumscribed about a square has twice the area of the circle\r\n" );
document.write( "inscribed in the square. \r\n" );
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document.write( "Edwin
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