document.write( "Question 1114707: The area of an equilateral triangle is 12cm2. The area of its inscribed circle is... \n" ); document.write( "
Algebra.Com's Answer #729622 by ikleyn(52781)\"\" \"About 
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document.write( "The expression for the area A of an equilateral triangle via its side length \"a\" is\r\n" );
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document.write( "A = \"a%5E2%2A%28sqrt%283%29%2F4%29\",  which gives\r\n" );
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document.write( "a^2 = \"%2812%2A4%29%2Fsqrt%283%29\" = \"%2812%2A4%2Asqrt%283%29%29%2F3\" = \"4%5E2%2Asqrt%283%29\"  ====>   a = \"4%2Aroot%284%2C3%29\".\r\n" );
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document.write( "Then the perimeter of the triangle is  P = 3a = \"12%2Aroot%284%2C3%29\".\r\n" );
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document.write( "Finally, the radius of the inscribed circle is  r = \"%282A%29%2FP\" = \"%282%2A4%2Aroot%284%2C3%29%29%2F%2812%2Aroot%284%2C3%29%29\" = \"8%2F12\" = \"2%2F3\" centimeters.\r\n" );
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document.write( "And the area of the inscribed circle is  \"pi%2Ar%5E2\" = \"pi%2A%282%2F3%29%5E2\" = \"4pi%2F9\"  cm^2.\r\n" );
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