+1855 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.
+1950 First, let's note that since the area of ABCD is 180, we have the equation
AD∗AB=180
Now, note that the shaded region is a trapezoid with base AB and UT, with height AD.
We know the length of AB and AD already, and UT is 1/3 the length of DC, so we are all set.
We can write the equation
(1/2)(AD)(AB+AB/3)=(1/2)(AD)(4/3)(AB)=(2/3)AD∗AB=(2/3)(180)=120
So our answer is 120.
Thanks! :)
+1950 First, let's note that since the area of ABCD is 180, we have the equation
AD∗AB=180
Now, note that the shaded region is a trapezoid with base AB and UT, with height AD.
We know the length of AB and AD already, and UT is 1/3 the length of DC, so we are all set.
We can write the equation
(1/2)(AD)(AB+AB/3)=(1/2)(AD)(4/3)(AB)=(2/3)AD∗AB=(2/3)(180)=120
So our answer is 120.
Thanks! :)
