document.write( "Question 78297: One angle of a rhombus is 120 degrees. The perimeter is 96m. Find the Area. \n" ); document.write( "
Algebra.Com's Answer #56181 by Edwin McCravy(20060)\"\" \"About 
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document.write( "One angle of a rhombus is 120 degrees. The perimeter\r\n" );
document.write( "is 96m.  Find the Area.\r\n" );
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document.write( "A rhombus is a parallelogram with all four sides equal:        \r\n" );
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document.write( "      _____________\r\n" );
document.write( "     /            /\r\n" );
document.write( "    /            /\r\n" );
document.write( "   /            /    \r\n" );
document.write( "  /            /\r\n" );
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document.write( "The formula for the area of any parallogram is bh\r\n" );
document.write( "So we draw in the height, h. The perimeter is 96,\r\n" );
document.write( "and since a rhombus has four equal sides, each side\r\n" );
document.write( "is 1/4 of 96m, or 24m.  Also since the measure\r\n" );
document.write( "of the obtuse interior angle on the lower right\r\n" );
document.write( "corner is 120°, the acute angle on the lower left\r\n" );
document.write( "corner must be supplementary to it, or 180°-120°\r\n" );
document.write( "which is 60°: \r\n" );
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document.write( "      _____________\r\n" );
document.write( "     /|   24m     /\r\n" );
document.write( "    / |          /\r\n" );
document.write( "24m/  |h        / 24m\r\n" );
document.write( "  /   |        /\r\n" );
document.write( " /60° |   120°/\r\n" );
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document.write( "Now from the right triangle on the left of the\r\n" );
document.write( "rhombus, \r\n" );
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document.write( "             h\r\n" );
document.write( "sin(60°) = ----\r\n" );
document.write( "            24\r\n" );
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document.write( "Multiply both sides by 24:\r\n" );
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document.write( "24·sin(60°) = h\r\n" );
document.write( "       _ \r\n" );
document.write( "   24(Ö3/2) = h\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "       12Ö3 = h\r\n" );
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document.write( "The formula for the area is\r\n" );
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document.write( "          A = base×height\r\n" );
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document.write( "The base is the bottom side which is 24m\r\n" );
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document.write( "The height is h which is 12Ö3\r\n" );
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document.write( "So        A = (24)(12Ö3)\r\n" );
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document.write( "          A = 288Ö3 or approximately 498.83063276\r\n" );
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document.write( "I'd round that off to 499m², or however your\r\n" );
document.write( "teacher tells you.\r\n" );
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document.write( "Edwin
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