document.write( "Question 1061892: In the given figure, the two rectangles EFGH and ACDE share a common corner at E and overlap so that BC = 7. What is the area of the shaded region ABGFEA?\r
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Algebra.Com's Answer #676676 by ikleyn(52803)\"\" \"About 
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\n" ); document.write( "In the given figure, the two rectangles EFGH and ACDE share a common corner at E and overlap so that BC = 7.
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document.write( "1.  Consider the quadrilateral ABHE (which is the intersection area of the original rectangles).\r\n" );
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document.write( "2.  Draw the diagonal BE in this quadrilateral.\r\n" );
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document.write( "    The length of the diagonal BE is  |BE| = \"sqrt%28abs%28AE%29%5E2%2Babs%28AB%29%5E2%29\" = \"sqrt%2812%5E2%2B1%5E2%29\" = \"sqrt%28145%29\".\r\n" );
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document.write( "3.  Therefore, the length of the segment BH is  |BH| = \"sqrt%28abs%28BE%29%5E2-abs%28HE%29%5E2%29\" = \"sqrt%28145-8%5E2%29\" = \"sqrt%2881%29\" = 9.\r\n" );
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document.write( "4.  The area of the triangle ABE is \"%281%2F2%29%2Aabs%28AB%29%2Aabs%28AE%29\" = \"%281%2F2%29%2A12%2A1\" = 6.\r\n" );
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document.write( "    The area of the triangle BHE is \"%281%2F2%29%2Aabs%28BH%29%2Aabs%28HE%29\" = \"%281%2F2%29%2A9%2A8\" = 36.\r\n" );
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document.write( "    Hence, the area of the quadrilateral ABHE is the sum of the areas of the triangles 6 + 36 = 42.\r\n" );
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document.write( "5.  Now the area of the shaded part under the question is 12*8 - 42 = 96-42 = 54.\r\n" );
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