As a general rule, we know that the area of a dilated figure is the area of the original figure multiplied by the square of the scale factor. We can see this in the following formula:
[tex]A=A^{\prime}\cdot k^2[/tex]where A is the area of the original figure, A' is the area of the dilated figure and k is the scale factor.
In this case, we have that the area of the dilated figure (trapezoid A'B'C') is 12 square units, and the scale factor is k = 2/3. Then, using the equation we get the following:
[tex]\begin{gathered} A^{\prime}=12 \\ k=\frac{2}{3} \\ \Rightarrow A=12\cdot(\frac{2}{3})^2=12\cdot(\frac{4}{9})=\frac{12\cdot4}{9}=\frac{48}{9}=5\frac{1}{3} \\ A=5\frac{1}{3}u^2 \end{gathered}[/tex]therefore, the area of trapezoid ABCD is 5 1/3 square units
