+1234 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.
+399 Note: I will use [] to denote area.
[ABCD] = AD * DC
[ADU] = [BCT] = AD*DU/2 = (AD*DC/3)/2=AD*DC/6
[ADU]+[BCT]=AD*DC/3
[ABTU] = [ABCD]-([ADU]+[BCT]) = 2/3*(AD*DC) = 120.
+399 Note: I will use [] to denote area.
[ABCD] = AD * DC
[ADU] = [BCT] = AD*DU/2 = (AD*DC/3)/2=AD*DC/6
[ADU]+[BCT]=AD*DC/3
[ABTU] = [ABCD]-([ADU]+[BCT]) = 2/3*(AD*DC) = 120.
