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數學難題 (Area and volume)

發問:

In the diagram, ABCD is a square of side 10 cm. Find the area of the shaded region PQRS. (Please show full steps and refrences, thx :P) 圖片參考：http://imgcld.yimg.com/8/n/HA00649033/o/701108040072413873437180.jpg

最佳解答:

Let AP = x and AQ = y, then: PD = 10 - x BQ = 10 - y DS = y - 4 CS = 14 - y BR = x + 3 RC = 7 - x So the total area of the 4 triangles is: (1/2) [(10 - y)(x + 3) + (7 - x)(14 - y) + xy + (10 - x)(y - 4)] = (1/2) (30 - 3y + 10x - xy + 98 - 14x + xy - 7y + xy + 10y - 40 - xy + 4x) = (1/2) (30 + 98 - 40) = 44 Hence the area of the shaded part is 100 - 44 = 56 cm2

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