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20 10 the answer and analysis of question 12 in the mathematics volume of Nanning senior high school entrance examination.
12. The locations of square ABCD, square BEFG and square RKPF are shown in Figure 4. G point is on DK line, and the side length of square BEFG is 4, so the area of triangle DEK is:

10(B) 12(C) 14(D) 16

Solution (d)

Let AB=X, FP=Y, extend PK, at point m.

∵ quadrilateral ABCD is a square.

∴AB=AD=CD=BC=X

∴S△AED=[(4+X)X]/2

∫CG = BC-BG = X-4

∴S△CGD=[(X-4)X]/2

∵ Quadrilateral FPRK is a square.

∴FR=RK=PK=FP=Y

GF = 4

∴S△KPG=[(4+Y)Y]/2

∫ quadrilateral FEBG and FPKR are squares.

∴∠MBG=∠BGP=∠P=90

∴ rectangular FPME

∴PM=4 KM=4-Y

EM = Y

∴S△EKM=[(4-Y)Y]/2

∴S△DKE=(S square ABCD+S square GFEB+S rectangular FPME)-(S△AED+

S△CGD+S△GPK+S△EMK)=(X∧2+ 16+4Y)-{[(4+X)X]/2+[(X-4)X]/2+[(4+Y)Y]/2+[(4-Y)Y]/2 }

Simplified S△DKE= 16