document.write( "Question 174202: finding the area of triangle ABC
\n" ); document.write( "a(3,4)
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\n" ); document.write( "A=the square root of s(s-a)(s-b)(s-c)
\n" ); document.write( "s=a+b+c divided by 2 \n" ); document.write( "
Algebra.Com's Answer #129184 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
finding the area of triangle ABC
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document.write( "Let's draw the triangle:\r\n" );
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document.write( "\"Area=sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29\"\r\n" );
document.write( "\"s=%28a%2Bb%2Bc%29%2F2\"\r\n" );
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document.write( "\"s\" stands for \"semi-perimeter\".\r\n" );
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document.write( "We find the length of each side using the distance\r\n" );
document.write( "formula:\r\n" );
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document.write( "To find \"a\", use the coordinates of its \r\n" );
document.write( "endpoints B and C: \r\n" );
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document.write( "\"matrix%281%2C3%2Ca%2C%22=%22%2Csqrt%28%287-5%29%5E2%2B%283-1%29%5E2%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Ca%2C%22=%22%2Csqrt%28%282%29%5E2%2B%282%29%5E2%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Ca%2C%22=%22%2Csqrt%284%2B4%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Ca%2C%22=%22%2Csqrt%288%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Ca%2C%22=%22%2Csqrt%284%2A2%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Ca%2C%22=%22%2Csqrt%284%29sqrt%282%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Ca%2C%22=%22%2C2sqrt%282%29=2.828427125%29\"\r\n" );
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document.write( "To find \"b\", use the coordinates of its \r\n" );
document.write( "endpoints A and C: \r\n" );
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document.write( "\"matrix%281%2C3%2Cb%2C%22=%22%2Csqrt%28%285-3%29%5E2%2B%281-4%29%5E2%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Cb%2C%22=%22%2Csqrt%28%282%29%5E2%2B%28-3%29%5E2%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Cb%2C%22=%22%2Csqrt%284%2B9%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Cb%2C%22=%22%2Csqrt%2813%29=3.605551275%29\"\r\n" );
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document.write( "To find \"c\", use the coordinates of its \r\n" );
document.write( "endpoints A and B: \r\n" );
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document.write( "\"matrix%281%2C3%2Cc%2C%22=%22%2Csqrt%28%287-3%29%5E2%2B%283-4%29%5E2%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Cc%2C%22=%22%2Csqrt%28%284%29%5E2%2B%28-1%29%5E2%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Cc%2C%22=%22%2Csqrt%2816%2B1%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Cc%2C%22=%22%2Csqrt%2817%29=4.123105626%29\"\r\n" );
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document.write( "\"s-a=5.278542013-2.828427125=2.450114888\"\r\n" );
document.write( "\"s-b=5.278542013-3.605551275=1.672990737\"\r\n" );
document.write( "\"s-c=5.278542013-4.123105626=1.155436387\"\r\n" );
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document.write( "So the area = 5.\r\n" );
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document.write( "However the easiest way to find the area is with a special\r\n" );
document.write( "determinant formula:\r\n" );
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document.write( "where the first two elements in each row of the \r\n" );
document.write( "determinant are the coordinates of the three points,\r\n" );
document.write( "and the last element in each row is 1.  That is, \r\n" );
document.write( "the last column contains all 1's.  Also notice that\r\n" );
document.write( "we must take the absolute value of the determinant,\r\n" );
document.write( "which is the reason for the double bars around the\r\n" );
document.write( "determinant.\r\n" );
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document.write( "Evaluate the 3x3 determinant.  I assume you know \r\n" );
document.write( "how if you want to use this method.\r\n" );
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document.write( "Edwin
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