document.write( "Question 1149554: What is the area of the rectangle? Show all work.\r
\n" ); document.write( "\n" ); document.write( "Coordinates: (-4, 0), (-6, 4), (4, 4), (2, 8)\r
\n" ); document.write( "\n" ); document.write( "Do not round anything until the very end.
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Algebra.Com's Answer #770902 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "1.  Make a sketch (making sketch is a necessary part of the solution to this problem (!) ).\r\n" );
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document.write( "2.  Conclude your figure into the smallest possible rectangle with horizontal and vertical sides.\r\n" );
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document.write( "    This rectangle has dimensions 10 (=4-(-6)) units horizontally and 8 (=8-0) units vertically, so its area is 80 square units.\r\n" );
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document.write( "3.  Cut (mentally) 4 right angled triangles from this large rectangle to get the smaller rectangle.\r\n" );
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document.write( "    The legs of these triangles are  2 and 4  units  and  8 and 4  units.\r\n" );
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document.write( "4.  So, from the area of the large rectangle you should subtract  the areas of these 4 triangles\r\n" );
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document.write( "         80 -  -  = 80 - 8 - 32 = 40.\r\n" );
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document.write( "Thus you get  the ANSWER  40 square units for the area of your rectangle\r\n" );
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document.write( "without using the distance formula and without calculating radicals.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This simple method often works for more complicated cases of arbitrary polygons, \r
\n" ); document.write( "\n" ); document.write( "if the vertices of a polygon lie in integer points of the coordinate grid.\r
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\n" ); document.write( "\n" ); document.write( "Using this approach, even 3-th or 4-th grade student is able to solve similar problems, even although he (or she)\r
\n" ); document.write( "\n" ); document.write( "doesn't know yet the distance formula and radicals.\r
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