document.write( "Question 1121762: ABCD is a square with diagonal AC 8 units long. How many square units are there in the area of the square? \n" ); document.write( "

Algebra.Com's Answer #737775 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "If \"a\" is the side length of a square, then the square of its diagonal is\r\n" );
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document.write( "   a^2 + a^2 = 2a^2,  according to Pythagoras.\r\n" );
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document.write( "From the other side, the area of such a square is a^2.\r\n" );
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document.write( "So, to calculate the area in your case, you need to square the diagonal and then divide it by 2:\r\n" );
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document.write( "    Area =  =  = 32 square units.\r\n" );
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document.write( "Answer.  The area of the given square is 32 square inches.\r\n" );
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document.write( "The diagonals divide the square in 4 congruent right angled triangles with the legs of the length 4 unit each.\r\n" );
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document.write( "So the area of each such triangle is   = 8 square units.\r\n" );
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document.write( "Then the area of the entire square is 4 times it, i.e. 4*8 = 32 square units - the same answer.\r\n" );
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