document.write( "Question 1044900: One side of a parallelogram is 10cm and its diagonals are 16m and 24cm respectively. Find its area \n" ); document.write( "

Algebra.Com's Answer #660364 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "One side of a parallelogram is 10cm and its diagonals are 16m and 24cm respectively. Find its area
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document.write( "1.  The area of a parallelogram is equal to half the product of its diagonals by the sine of the angle between them:\r\n" );
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document.write( "    S = .\r\n" );
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document.write( "    See the lesson Area of a parallelogram in this site.\r\n" );
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document.write( "    Any of the two angles is good.\r\n" );
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document.write( "2.  You have the diagonals, and all you need is the sine of the angle between the diagonals.\r\n" );
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document.write( "    Instead of sine, we can find the cosine of the angle between the diagonals.\r\n" );
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document.write( "    For it, we will use the Cosine Law by applying it to the triangle formed by halves of diagonals and the side of the parallelogram:\r\n" );
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document.write( "     = .\r\n" );
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document.write( "    Which gives   =  = .\r\n" );
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document.write( "    And then  =  =  =  =  =  =  =  = .\r\n" );
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document.write( "4.  Finally, the area of the parallelogram is\r\n" );
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document.write( "    S =  =  = 58.095  (approximately).\r\n" );
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document.write( "Answer.  The area of the parallelogram is   = 58.095  (approximately).\r\n" );
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