document.write( "Question 557109: Four squares with sides 4, 3, 2 and 1 cm are placed side by side left to right, lower part of the squares are connected forming a base (one line). There is a diagonal line from the top left corner of the side 4 cm square to the bottom right of the side 1 cm square. Calculate the area of the trapezoid inside the triangle (diagonal line) of the 3 cm square. \n" ); document.write( "
Algebra.Com's Answer #362481 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let's chop off the tops and use some lettering:\r\n" );
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document.write( "We want to find the area of trapezoid DEFG.\r\n" );
document.write( "The formula for the area of a trapezoid is\r\n" );
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document.write( "Area = \"%28h%28b%5B1%5D+%2B+b%5B2%5D%29%29%2F2\"\r\n" );
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document.write( "which with this choice of letters that formula becomes:\r\n" );
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document.write( "Area = \"%28EF%28DE+%2B+FG%29%29%2F2\"\r\n" );
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document.write( "and we are given that EF = 3, so the formula further becomes\r\n" );
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document.write( "Area = \"%283%28DE+%2B+FG%29%29%2F2\"\r\n" );
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document.write( "So we just need DE and FG\r\n" );
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document.write( "The problem is done with similar triangles.\r\n" );
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document.write( "ᐃDEC ∼ ᐃGFC ∼ ᐃABC\r\n" );
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document.write( "AB = 4 (given)\r\n" );
document.write( "BC = BE+EF+FH+HC = 4+3+2+1 = 10, \r\n" );
document.write( "EC = EF+FH+HC = 3+2+1 = 6, \r\n" );
document.write( "FC = FH+HC = 2+1 = 3\r\n" );
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document.write( "Using ᐃDEC ∼ ᐃABC\r\n" );
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document.write( "\"%28DE%29%2F%28EC%29\" = \"%28AB%29%2F%28BC%29\"\r\n" );
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document.write( "\"%28DE%29%2F6\" = \"4%2F10\"\r\n" );
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document.write( "10·DE = 4·6\r\n" );
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document.write( "10·DE = 24\r\n" );
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document.write( "   DE = \"24%2F10\"\r\n" );
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document.write( "   DE = 2.4\r\n" );
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document.write( "Using ᐃGFC ∼ ᐃABC\r\n" );
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document.write( "\"%28FG%29%2F%28FC%29\" = \"%28AB%29%2F%28BC%29\"\r\n" );
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document.write( "\"%28FG%29%2F3\" = \"4%2F10\"\r\n" );
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document.write( "10·FG = 4·3\r\n" );
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document.write( "10·FG = 12\r\n" );
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document.write( "   FG = \"12%2F10\"\r\n" );
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document.write( "   FG = 1.2\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "Area = \"%283%28DE+%2B+FG%29%29%2F2\"\r\n" );
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document.write( "Area = \"%283%282.4+%2B+1.2%29%29%2F2\"\r\n" );
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document.write( "Area = \"%283%283.6%29%29%2F2\"\r\n" );
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document.write( "Area = 5.4 cm²\r\n" );
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document.write( "Edwin
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