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If two figures are similar the ratio of their areas is the same as the ratios of the squares of the corresponding sides.

 

PS and AD are corresponding sides; the squares of their ratio is:  27.5² / 11² 

 

The ratio of the area of PQRS to the area of ABCD is x / 54

 

Setting these two equal:  x / 54  =  27.5² / 11²    --->     x  =  54 · 27.5² / 11²