The centroid of the trapezoidal with its one face perpendicular is given be

X=-1/3 (-2b^2-2ab+a^2)/(a+b)

Y=1/3 h (b+2a)/(a+b)

Where a, b, h and origin is as shown in the figure below.

Similarly, the centroid of any trapezoidal is given by

x= 1/3(3ab+3bc+b^2+6ac+3a^2+2c^2)/(b+2a+c)

y=1/3 h (b+3a+c)/(b+2a+c)

Where a, b ,c, h and origin is as shown in the figure below.

The result was obtained using MathLab 7.0