document.write( "Question 1195091: The lengths indicated on the rectangle shown are in centimeters. What is the number of square centimeters in the area of the shaded region? \n" ); document.write( "

Algebra.Com's Answer #827453 by ikleyn(52810) $\"\"$ $\"About$

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document.write( "The given BIGGEST rectangle has dimensions 2+6 = 8 units by 9+5 = 14 units.\r\n" );
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document.write( "If the left lover corner of this rectangle is (0,0), the origin, then OBVIOUSLY, \r\n" );
document.write( "the center point of the rectangle is (7,4).\r\n" );
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document.write( "The area of the big rectangle is 8*14 square units, and 1/4 of its area is  = 28 square units.\r\n" );
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document.write( "    OK.  Let's consider the shaded quadrilateral.\r\n" );
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document.write( "Then it is OBVIOS that the area of the shaded quadrilateral is equal to 1/4 of the area \r\n" );
document.write( "of the BIG rectangle plus the area of the adjacent \"vertical\" right-angled triangle \r\n" );
document.write( "minus the area of the adjacent \"horizontal\" right angled triangle.   (*)\r\n" );
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document.write( "Adjacent \"vertical\" triangle has the legs 8-4 = 4 units (vertical) and 9-7 = 2 units (horizontal);\r\n" );
document.write( "so its area is  (1/2)*4*2 = 4 square units.\r\n" );
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document.write( "Adjacent \"horizontal\" triangle has the legs 8-4-2 = 2 units (vertical) and 14-7 = 7 units (horizontal);\r\n" );
document.write( "so its area is  (1/2)*2*7 = 7 square units.\r\n" );
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document.write( "Therefore, the area of the shaded region, according to the wording formula (*) is\r\n" );
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document.write( "    28 + 4 - 7 = 25 square units.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Actually, to solve the problem, this three-steps simple instruction is enough:\r
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document.write( "    (1)  take one fourth of the area of the big rectangle;\r\n" );
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document.write( "    (2)  add the area of the adjacent \"vertical\" right-angled triangle;\r\n" );
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document.write( "    (3)  subtract the area of the adjacent \"horizontal\" right-angled triangle.\r\n" );
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