數學難題 (Area and volume)

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