document.write( "Question 485997: A pentagon has vertices of (10,0), (5,8), (0,12), (-6,0) and (0,-6). What fraction of its total area lies in the 4th quadrant? \n" ); document.write( "
Algebra.Com's Answer #332302 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We draw the pentagon:\r\n" );
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document.write( "There are two ways of doing this, depending on what you have\r\n" );
document.write( "studied.  If you have studied finding the area of a convex\r\n" );
document.write( "polygon by means of a determinant, then post again and I will\r\n" );
document.write( "show you that method.  But I will assume you haven't had that\r\n" );
document.write( "yet and need to break the area down into right triangles and\r\n" );
document.write( "a rectangle.\r\n" );
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document.write( "We petition off the pentagon into 5 right triangles\r\n" );
document.write( "and 1 rectangle:\r\n" );
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document.write( "The Area of a triangle is\r\n" );
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document.write( "A = \"1%2F2\"bh\r\n" );
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document.write( "We find area of right triangle #1:\r\n" );
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document.write( "Right triangle #1 has base 6 and height 12. Substituting\r\n" );
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document.write( "A = \"1%2F2\"bh = \"1%2F2\"(6)(12) = 36\r\n" );
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document.write( "We find area of right triangle #2:\r\n" );
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document.write( "Right triangle #2 has base 5 and height 4. Substituting\r\n" );
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document.write( "A = \"1%2F2\"bh = \"1%2F2\"(5)(4) = 10\r\n" );
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document.write( "Rectangle #3 is 8 by 5, so its area is 8×5 or 40\r\n" );
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document.write( "We find area of right triangle #4:\r\n" );
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document.write( "Right triangle #4 has base 5 and height 8. Substituting\r\n" );
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document.write( "A = \"1%2F2\"bh = \"1%2F2\"(5)(8) = 20\r\n" );
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document.write( "We find area of right triangle #5:\r\n" );
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document.write( "Right triangle #5 has base 6 and height 6. Substituting\r\n" );
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document.write( "A = \"1%2F2\"bh = \"1%2F2\"(6)(6) = 18\r\n" );
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document.write( "We find area of right triangle #6:\r\n" );
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document.write( "Right triangle #6 has base 10 and height 6. Substituting\r\n" );
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document.write( "A = \"1%2F2\"bh = \"1%2F2\"(10)(6) = 30\r\n" );
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document.write( "The area of the entire pentagon is\r\n" );
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document.write( "#1 has area 36\r\n" );
document.write( "#2 has area 10\r\n" );
document.write( "#3 has area 40\r\n" );
document.write( "#4 has area 20\r\n" );
document.write( "#5 has area 18\r\n" );
document.write( "#6 has area 30\r\n" );
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document.write( "total =    154\r\n" );
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document.write( "The area that lies in the 4th quadrant is right\r\n" );
document.write( "triangle #6, which has area 30.\r\n" );
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document.write( "Therefore the fraction of the total area that lies\r\n" );
document.write( "in the 4th quadrant is \"30%2F154\"\r\n" );
document.write( "which reduces to \"15%2F77\"\r\n" );
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document.write( "Edwin

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