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