document.write( "Question 1060916: Find the perimeter in inches of a regular polygon whose area is 24 square root 3 inches, and whose apothem, the perpendicular distance from the center of the regular polygon to one of its sides, is 2 square root 3 inches. \n" ); document.write( "

Algebra.Com's Answer #675773 by ikleyn(52809) $\"\"$ $\"About$

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\n" ); document.write( "Find the perimeter in inches of a regular polygon whose area is 24 square root 3 $\"highlight%28square%29\"$ inches, and whose apothem,
\n" ); document.write( "the perpendicular distance from the center of the regular polygon to one of its sides, is 2 square root 3 inches.
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document.write( "The area of this regular polygon (of every regular polygon, actually) is half of the product of its perimeter by the apothem:\r\n" );
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document.write( "A = .   (1)\r\n" );
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document.write( "You easily can get (can prove) this formula by drawing the segments from the center of the polygon to all its vertices. \r\n" );
document.write( "The segments divide the polygon into the union of congruent triangles. By applying the formula for the area of every single triangle, \r\n" );
document.write( "you sum up their areas to the right side of the formula (1).\r\n" );
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document.write( "Now, from (1) you have P =  =  = 24 inches.\r\n" );
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document.write( "Answer.  The perimeter = 24 inches.\r\n" );
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