document.write( "Question 1063362: area of an inscribed semi circle in an equilateral triangle\r
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Algebra.Com's Answer #678470 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "1.  Make a sketch. Draw an equilateral triangle; an inscribed semi-circle; and the radius from the center of the semi-circle \r\n" );
document.write( "    to the tangent point on the triangle side.\r\n" );
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document.write( "    Notice that this radius is the height in the right-angled triangle which has the triangle side as the hypotenuse.\r\n" );
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document.write( "2.  Let \"a\" be the side length of the equilateral triangle.\r\n" );
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document.write( "    Then its area is  = .\r\n" );
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document.write( "3.  From the other side, the area of the equilateral triangle is twice the area of the right-angled triangle  = ar.\r\n" );
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document.write( "    Thus you get the equation \r\n" );
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document.write( "     = ar,\r\n" );
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document.write( "    which gives you  r = .\r\n" );
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