document.write( "Question 1210155: ABCE is a Parallelogram. ADEF is a Rhombus. Find the area of the composite figure.
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Algebra.Com's Answer #851414 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We calculate GE by using the Pythagorean theorem on right triangle FGE.\r\n" );
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document.write( "\"GE=sqrt%2817%5E2-5%5E2%29=sqrt%28264%29=sqrt%284%2A66%29=2sqrt%2866%29\"\r\n" );
document.write( "AG is also \"2sqrt%2866%29\", so diagonal of the rhombus, AE = \"4sqrt%2866%29\"\r\n" );
document.write( "FG = GD = 5 so the other diagonal of the rhombus, FD is 10.\r\n" );
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document.write( "The area of a rhombus is \"1%2F2\" the product of the diagonals, or,\r\n" );
document.write( "Area of rhombus ADEF is \"expr%281%2F2%29%2AAE%2AFD=expr%281%2F2%29%2A4sqrt%2866%29%2A10=20sqrt%2866%29\".\r\n" );
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document.write( "Since ABCF is a parallellogram, \r\n" );
document.write( "ABCD is an isosceles trapezoid (or trapezium if you live in the UK).\r\n" );
document.write( "We draw two green lines at D and C perpendicular to AB and CD. They partition\r\n" );
document.write( "the trapezoid into two congruent right triangles, and a rectangle in the middle.\r\n" );
document.write( "Since AH = GD = 5, the area of right triangle AHD is\r\n" );
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document.write( "The area of right triangle BIC is also \"5sqrt%2866%29\"\r\n" );
document.write( "All that's left of isosceles trapezoid ABCD is the area of rectangle HICD which\r\n" );
document.write( "is \r\n" );
document.write( "Area of rectangle = \"22sqrt%2866%29\"\r\n" );
document.write( "Area of right triangle BIC = \"5sqrt%2866%29\"\r\n" );
document.write( "Area of isosceles trapezoid ABCD = \"32sqrt%2866%29\"\r\n" );
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document.write( "Area of rhombus ADEF = \"20sqrt%2866%29\"\r\n" );
document.write( "Area of isosceles trapezoid ABCD = \"32sqrt%2866%29\"\r\n" );
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document.write( "Area of composite figure = \"52sqrt%2866%29\"\r\n" );
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document.write( "That's approximately 422.4 sqruare units.\r\n" );
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document.write( "Edwin
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