document.write( "Question 1186474: ABCD is a square with side of 10 cm. 3 points Square PQRS is drawn inside the square ABCD such that trapezoids PQBA, QRCB, SRCD and PSDA are equal. If the area of the trapezoid is 16 cm^2, find the height of the trapezium. \n" ); document.write( "
Algebra.Com's Answer #817395 by ikleyn(52824)\"\" \"About 
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\n" ); document.write( "ABCD is a square with side of 10 cm. \"highlight%28cross%283_points%29%29\" Square PQRS is drawn inside the square ABCD
\n" ); document.write( "such that trapezoids PQBA, QRCB, SRCD and PSDA are equal.
\n" ); document.write( "If the area of the trapezoid is 16 cm^2, find the height of the trapezium.
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document.write( "From the area of the square ABCD, subtract four times the area of the trapezoid to get the area of the square PQRS\r\n" );
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document.write( "    the area of the square PQRS = 10^2 - 4*16 = 100 - 64 = 36 cm^2.\r\n" );
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document.write( "Hence, the side of the square PQRS is  \"sqrt%2836%29\" = 6.\r\n" );
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document.write( "Since the trapezoids are equal (congruent), it means that the strip between the squares is of uniform width of  \"%2810+-+6%29%2F2\" cm = \"4%2F2\" = 2 cm.\r\n" );
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document.write( "The width of the strip is the height of the trapezoids.\r\n" );
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document.write( "ANSWER.  The height of the trapezoids is 2 cm.\r\n" );
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\n" ); document.write( "\n" ); document.write( "These words in the condition of the problem\r
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document.write( "    \"highlight%28cross%283_points%29%29\" Square PQRS \r\n" );
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\n" ); document.write( "\n" ); document.write( "perplexed me, when I read this problem today in the morning . . . \r
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