document.write( "Question 205893: PQRS is a trapezium where PQ // SR. Given that PQR = SPR= 90˚, PQ = 8.5cm and PR = 12.3 cm. Calculate (a) QR (b) PS (c) The area of the trapezium PQRS.\r
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Algebra.Com's Answer #155503 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
PQRS is a trapezium where PQ // SR. Given that PQR = SPR= 90˚, PQ = 8.5cm and PR = 12.3 cm. Calculate (a) QR (b) PS (c) The area of the trapezium PQRS.
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document.write( "You must be from the UK. In the US we say \"trapezoid\" and \"math\",\r\n" );
document.write( "and you say \"trapezium\" and \"maths\".  :)\r\n" );
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document.write( "We can find QR by the Pythagorean theorem:\r\n" );
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document.write( "\"PQ%5E2%2BQR%5E2=PR%5E2\"\r\n" );
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document.write( "\"8.5%5E2%2BQR%5E2+=+12.3%5E2\"\r\n" );
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document.write( "\"72.25%2BQR%5E2=151.29\"\r\n" );
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document.write( "\"QR%5E2=79.04\"\r\n" );
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document.write( "\"QR=sqrt%2879.04%29\"\r\n" );
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document.write( "\"QR=8.890444308\"\r\n" );
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document.write( "Angles QPR and PRS are equal in measurement because they are alternate\r\n" );
document.write( "interior angles formed by transversal PR intersecting two given parallel\r\n" );
document.write( "line segments PQ and SR. And we are given that PQR = SPR = 90˚.  Therefore,\r\n" );
document.write( "right triangles PQR and RPS are similar triangles.  Therefore their\r\n" );
document.write( "sides are proportional, so we set up the proportion:\r\n" );
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document.write( "So:\r\n" );
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document.write( "\"PS%2FQR=PR%2FPQ\" \r\n" );
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document.write( "\"PS%2F8.890444308=12.3%2F8.5\"\r\n" );
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document.write( "Solve that proportion equation and get  \r\n" );
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document.write( "\"PS+=+12.86499588\"\r\n" );
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document.write( "We find the areas of both triangles and add them.\r\n" );
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document.write( "To find the area of triangle PQR, we use formula\r\n" );
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document.write( "\"Area=base%2Aheight%2F2\"\r\n" );
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document.write( "\"Area=PQ%2AQR%2F2=8.5%2A8.890444308%2F2=37.78438831cm%5E2\"\r\n" );
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document.write( "To find the area of triangle RPS, we use formula\r\n" );
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document.write( "\"Area=base%2Aheight%2F2\"\r\n" );
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document.write( "\"Area=PS%2APR%2F2=12.86499588%2A12.3%2F2=79.11972467cm%5E2\"\r\n" );
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document.write( "Adding those areas together:\r\n" );
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document.write( "\"37.78438831cm%5E2%2B79.11972467cm%5E2=116.904113cm%5E2\"\r\n" );
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document.write( "Edwin
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