In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded region.
Total area = DC * AD
Area of triangles ADU + BCT = 2* (1/2)( DC/3) (AD) = DC * AD / 3
Shaded area = DC*AD - DC * AD / 3 = (2/3)DC *AD = (2/3)(180) = 120
+359 
