SMC2012_web_solutions

Pqrs area pqts area qrt 9 3 4 3 2 3 3 2 2 1 3 1 3 3 2

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PQRS ) = area( PQTS ) + area( QRT ) 9 3 4 3 2 3 3 2 2 1 3 1 3 3 2 ) ( = × + × = . Alternatively, as PQ is parallel to SR , PQRS is a trapezium. We now use the fact that the area of a trapezium is its height multiplied by the average length of its parallel sides. Hence, PQRS has area. ) 1 ( 3 1 2 1 3 3 2 + × 9 3 4 3 2 3 3 2 = × = . The tile is made up of three copies of PQRS. So its area is . 3 3 3 4 9 3 4 = × 1 1 1 1 1 1
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