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.
AD * AB =180
The shaded area is a trapezoid with bases of AB, AB/3 and height AD
Its area =
(1/2)(AD)(AB + AB/3) =
(1/2)(AD)(4/3)(AB) =
(2/3) AD * AB = (2/3)(180) = 120
+1459 
