document.write( "Question 1190321: In parallelogram ABCD, AB = 13, AD = 14, and the length of diagonal AC is 15. What is the area of the parallelogram in square units? \n" ); document.write( "

Algebra.Com's Answer #821940 by ikleyn(52864) $\"\"$ $\"About$

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\n" ); document.write( "In parallelogram ABCD, AB = 13, AD = 14, and the length of diagonal AC is 15.
\n" ); document.write( "What is the area of the parallelogram in square units?
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document.write( "Apply the cosine law and find cosine of the angle B between the sides AB and BC of the parallelogram\r\n" );
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document.write( "(the diagonal AC is the opposite side of the triangle ABC to angle B)\r\n" );
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document.write( "    AC^2 = AB^2 + BC^2 - 2*AB*BC*cos(B)\r\n" );
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document.write( "    15^2 = 13^2 + 14^2 - 2*13*14*cos(B)\r\n" );
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document.write( "    cos(B) =  =  = .\r\n" );
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document.write( "Next, find sin(B) = =  =  = .\r\n" );
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document.write( "Finally, find the area of the parallelogram ABCD\r\n" );
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document.write( "     = AB*BC*sin(B) =  = 14*12 = 168 square units.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved. // An amazing phenomenon is that this answer is a precise integer number ( ! )\r
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\n" ); document.write( "\n" ); document.write( "Another way to solve the problem is to find the area of the triangle ABC using\r
\n" ); document.write( "\n" ); document.write( "the Heron's formula (the lengths of the sides of the triangle are given ( ! ) ).\r
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\n" ); document.write( "\n" ); document.write( "After finding the area of the triangle ABC simply double it,
\n" ); document.write( "and you will get the area of the parallelogram ABCD.\r
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