document.write( "Question 1209089: ABCDEF is a regular hexagon, and PQR is an equilateral triangle. Find the ratio of the area of the triangle to the area of the hexagon.
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Algebra.Com's Answer #847663 by ikleyn(52798) $\"\"$ $\"About$

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document.write( "Let r be the side of the hexagon ABCDEF.\r\n" );
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document.write( "Then the area of the hexagon is the area of 6 equilateral triangles with the side \"r\"\r\n" );
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document.write( "    area of the hexagon = .\r\n" );
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document.write( "Regarding the triangle PQR, its side is, OBVIOUSLY, arithmetic mean of r and 2r\r\n" );
document.write( "(its side is the mid-line of the trapezoid CDEB).\r\n" );
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document.write( "So, the side of the triangle PQR is  a =  = 1.5r.\r\n" );
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document.write( "Then the area of the triangle PQR is   = .\r\n" );
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document.write( "Thus the ratio of the area of the triangle to the area of the hexagon is\r\n" );
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document.write( "     =  =  =  = .    ANSWER\r\n" );
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