document.write( "Question 601773: Find the area of an octagon with a side length of 4 inches. \n" ); document.write( "
Algebra.Com's Answer #380162 by Edwin McCravy(20056)\"\" \"About 
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document.write( "A regular octagon is a square with the 4 isosceles right triangles\r\n" );
document.write( "chopped off the corners as you see below.\r\n" );
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document.write( "One side of the square is x+4+x or 2x+4.\r\n" );
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document.write( "So the area of the square is (2x+4)²\r\n" );
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document.write( "We look at one of the four isosceles triangles that we are to cut\r\n" );
document.write( "off the corners of the square.\r\n" );
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document.write( "We use the Pythagoreant theorem to find side 8:\r\n" );
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document.write( "x² + x² = 4²\r\n" );
document.write( "    2x² = 16\r\n" );
document.write( "     x² = 8\r\n" );
document.write( "      x = \"sqrt%288%29\"\r\n" );
document.write( "      x = \"sqrt%284%2A2%29\"\r\n" );
document.write( "      x = \"2sqrt%282%29\"\r\n" );
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document.write( "So the area of the square is\r\n" );
document.write( "                 _            _             _              _\r\n" );
document.write( "(2x + 4)² = (2*2V2 + 4)² = (4V2 + 4)² = [4(V2 + 1)]² = 16(V2 + 1)² sq. in.\r\n" );
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document.write( "The area of one of the triangles is:\r\n" );
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document.write( "\"1%2F2\"·base·height = \"1%2F2\"·x·x = \"1%2F2\"·x² = \"1%2F2\"·8 = 4 sq. in.\r\n" );
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document.write( "So the 4 triangles that we cut from the square have total area of \r\n" );
document.write( "4·4 or 16 sq. in.\r\n" );
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document.write( "Therefore the area of the regular octagon is\r\n" );
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document.write( "Area of square minus area of the four triangles =\r\n" );
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document.write( "16(Ö2 + 1)² - 16 = \r\n" );
document.write( "     _\r\n" );
document.write( "16[(Ö2 + 1)² - 1] = \r\n" );
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document.write( "16[2 + 2Ö2 + 1 - 1] = \r\n" );
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document.write( "16[2 + 2Ö2] =\r\n" );
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document.write( "16[2(1 + Ö2) =\r\n" );
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document.write( "32(1 + Ö2) or about 77.25 sq. in. \r\n" );
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document.write( "Edwin
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