document.write( "Question 1068016: In hexagon ABCDEF, AB = DE = 2, BC = EF = 4$, CD = FA = 6, and all the interior angles are equal. Find the area of hexagon ABCDEF. \n" ); document.write( "
Algebra.Com's Answer #683570 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "It's easy to show by the formula for the sum of the angles that\r\n" );
document.write( "each interior angle is 120°, whose supplement is 60°.\r\n" );
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document.write( "Now we draw in some green lines to enclose the hexagon in a rectangle.\r\n" );
document.write( "We have added four 30°-60°-90° right triangles to the hexagon.\r\n" );
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document.write( "In a 30°-60°-90° right triangle the shorter leg\r\n" );
document.write( "is one-half of the hypotenuse.  And the longer leg\r\n" );
document.write( "is the shorter leg times √3.\r\n" );
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document.write( "Since we know all 4 hypotenuses, we can find the dimensions\r\n" );
document.write( "of the enclosing rectangle. \r\n" );
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document.write( "The area of the big rectangle is \r\n" );
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document.write( "(length)(width)= (9)(3√3) = 27√3\r\n" );
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document.write( "The area of each of the two larger 30°-60°-90° right triangles\r\n" );
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document.write( "(base)(height)/2 = (2)(2√3)/2 = 2√3\r\n" );
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document.write( "The area of both of them is 4√3\r\n" );
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document.write( "The area of each of the two smaller 30°-60°-90° right triangles\r\n" );
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document.write( "(base)(height)/2 = 1(√3)/2 = √3/2\r\n" );
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document.write( "The area of both of them is √3\r\n" );
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document.write( "We get the area of the hexagon by subtracting the\r\n" );
document.write( "areas of the 4 right triangles:\r\n" );
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document.write( "27√3 - 4√3 - √3 = 22√3\r\n" );
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document.write( "Edwin
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