document.write( "Question 1023585: a trapezium has a sides of 12, 12, 15 respectively and an [included] angle of 90°. find the surface area of the one side of the trapezium.\r
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Algebra.Com's Answer #639140 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "A four-sided polygon with exactly one pair of parallel sides is\r\n" );
document.write( "called \"a trapezoid\" in US English and \"a trapezium\" in UK English.\r\n" );
document.write( "One with sides 12, 12, 15 an [included] angle of 90° must be this: \r\n" );
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document.write( "Since it has one [included] angle of 90° then it\r\n" );
document.write( "must contain another one as well.\r\n" );
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document.write( "But these instructions make no sense:\r\n" );
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document.write( "\"find the surface area of the one side of the trapezium.\"\r\n" );
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document.write( "\"Surface area\" is used for 3-dimensional figures, not \r\n" );
document.write( "2-dimensional figures.  And \"sides\" only have length, not\r\n" );
document.write( "area.\r\n" );
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document.write( "Maybe you mean:\r\n" );
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document.write( "(a) \"What is the length of the fourth side of the trapezium?\"\r\n" );
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document.write( "and\r\n" );
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document.write( "(b) \"What is the area of the trapezium?\"\r\n" );
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document.write( "To answer those questions we draw in this green line\r\n" );
document.write( "altitude, which also has length 12:\r\n" );
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document.write( "We calculate the bottom side of the right triangle\r\n" );
document.write( "by using the Pythagorean theorem.\r\n" );
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document.write( "\"a%5E2%2Bb%5E2=c%5E2\"\r\n" );
document.write( "\"12%5E2%2Bb%5E2=15%5E2\"\r\n" );
document.write( "\"144%2Bb%5E2=225\"\r\n" );
document.write( "\"b%5E2=81\"\r\n" );
document.write( "\"b=sqrt%2881%29\"\r\n" );
document.write( "\"b=9\"\r\n" );
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document.write( "So the bottom side of the right triangle is 9.\r\n" );
document.write( "The rest of the bottom side of the trapezium is the\r\n" );
document.write( "same length as the top side of the trapezium or 12.\r\n" );
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document.write( "Therefore the bottom side of the trapezium is\r\n" );
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document.write( "12+9 or 21.\r\n" );
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document.write( "The area of the trapezoid can either be calculated\r\n" );
document.write( "using the formula:\r\n" );
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document.write( "\"A\"\"%22%22=%22%22\"\"expr%28%28a%2Bb%29%2F2%29%2Ah\"\r\n" );
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document.write( "where a and b are the two parallel sides of the trapezium,\r\n" );
document.write( "and h is the perpendicular distance between them:\r\n" );
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document.write( "\"A\"\"%22%22=%22%22\"\"expr%28%2812%2B21%29%2F2%29%2A12\"\r\n" );
document.write( "\"A\"\"%22%22=%22%22\"\"198\"\r\n" );
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document.write( "Or else you can find the area of the square, which is \r\n" );
document.write( "12x12 = 144\r\n" );
document.write( "and add the area of the right triangle, which is\r\n" );
document.write( "\"A\"\"%22%22=%22%22\"\"expr%28%281%29%2F2%29%2Ab%2Ah\"\r\n" );
document.write( "\"A\"\"%22%22=%22%22\"\"expr%28%281%29%2F2%29%2A9%2A12\"\r\n" );
document.write( "\"A\"\"%22%22=%22%22\"\"54\"\r\n" );
document.write( "And get \r\n" );
document.write( "\"144%2B54=198\"\r\n" );
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document.write( "Edwin
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