document.write( "Question 1210154: ABCG is a trapezoid.
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Algebra.Com's Answer #851406 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "My drawing is not quite to scale, because GCDE doesn't quite\r\n" );
document.write( "look like a rhombus.\r\n" );
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document.write( "I labeled two more points than the drawing on the site, H and I. \r\n" );
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document.write( "Area of rhombus GCDE is half the product of the diagonals.\r\n" );
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document.write( "\"expr%281%2F2%29%2ADG%2ACE+=+expr%281%2F2%29%282%2A7%29%282%2A4%29=56\"\r\n" );
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document.write( "Area of triangle EFG is half the base times height\r\n" );
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document.write( "Now all we need is the area of trapezoid ABCG.\r\n" );
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document.write( "We must find CG. \r\n" );
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document.write( "The diagonals of a rhombus are perpendicular, and therefore triangle CIG\r\n" );
document.write( "is a right triangle. GI = DI = 7, and IC = 4, so\r\n" );
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document.write( "\"CG+=+sqrt%28GI%5E2%2BIC%5E2%29=sqrt%287%5E2%2B4%5E2%29=sqrt%2849%2B16%29=sqrt%2865%29\"\r\n" );
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document.write( "The area of a trapezoid is the average base times the height:\r\n" );
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document.write( "The average base of trapezoid ABCG is \"%28AB%2BCG%29%2F2+=%2814%2Bsqrt%2865%29%29%2F2\"\r\n" );
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document.write( "The height of trapezoid is 6, so the area of trapezoid ABCG is\r\n" );
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document.write( "\"6%2Aexpr%28%2814%2Bsqrt%2865%29%29%2F2%29=3%2814%2Bsqrt%2865%29%29=42%2B3sqrt%2865%29\"\r\n" );
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document.write( "So we add the three areas together:\r\n" );
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document.write( "Area of trapezoid ABCG = \"3%2814%2Bsqrt%2865%29%29\"\r\n" );
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document.write( "Area of rhombus GCDE = 56\r\n" );
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document.write( "Area of triangle EFG = 100\r\n" );
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document.write( "Answer = \"42%2B3sqrt%2865%29%29%2B56%2B100\"\r\n" );
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document.write( "Area of rhombus GCDE is half the product of the diagonals.\r\n" );
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document.write( "\"expr%281%2F2%29%2ADG%2ACE+=+expr%281%2F2%29%282%2A7%29%282%2A4%29=56\"\r\n" );
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document.write( "Area of triangle EFG is half the base times height\r\n" );
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document.write( "Now all we need is the area of trapezoid ABCG.\r\n" );
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document.write( "We must find CG. \r\n" );
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document.write( "The diagonals of a rhombus are perpendicular, and therefore triangle CIG\r\n" );
document.write( "is a right triangle. GI = DI = 7, and IC = 4, so\r\n" );
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document.write( "\"CG+=+sqrt%28GI%5E2%2BIC%5E2%29=sqrt%287%5E2%2B4%5E2%29=sqrt%2849%2B16%29=sqrt%2865%29\"\r\n" );
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document.write( "The area of a trapezoid is the average base times the height:\r\n" );
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document.write( "The average base of trapezoid ABCG is \"%28AB%2BCG%29%2F2+=%2814%2Bsqrt%2865%29%29%2F2\"\r\n" );
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document.write( "The height of trapezoid is 6, so the area of trapezoid ABCG is\r\n" );
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document.write( "\"6%2Aexpr%28%2814%2Bsqrt%2865%29%29%2F2%29=3%2814%2Bsqrt%2865%29%29=42%2B3sqrt%2865%29\"\r\n" );
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document.write( "So we add the three areas together:\r\n" );
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document.write( "Area of trapezoid ABCG = \"42%2B3sqrt%2865%29\"\r\n" );
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document.write( "Area of rhombus GCDE = 56\r\n" );
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document.write( "Area of triangle EFG = 100\r\n" );
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document.write( "Answer = \"42%2B3sqrt%2865%29%2B56%2B100+=+198+%2B+3sqrt%2865%29\" cm2\r\n" );
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document.write( "That's approximately 222.2 cm2 \r\n" );
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document.write( "Edwin
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