+1839 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.
+1926 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! :)
+1926 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! :)
