Drawing a diagram, we can see the square ABCD is divided up into four shapes, APR,BQP, PQR and CDRQ.
So a simple way to work out the area of PQR is to work out the area of ABCD then take away the areas of the other shapes inside.
Area(ABCD)= length^{2} =6^{2} = 36
Area(APR) = Base*Height/2 = 2*4/2 = 4
Area(BQP) = Base*Height/2 = 3*4/2 = 6
Area(CDRQ) = Height*(side+opposite side)/2 = 6*(3+2)/2 = 15
Therefore Area(PQR) = 36 - 4 - 6 - 15 = 11cm^{2}