ANSWER:
The area of the dilated trapezoid is 12 cm^2.
STEP-BY-STEP EXPLANATION:
We have that the formula for the area of a trapezoid is:
[tex]A=\frac{(b+B)}{2}\cdot h[/tex]The scale factor is 4, therefore we multiply each value by 4:
[tex]\begin{gathered} A=\frac{(4b+4B)}{2}\cdot4h \\ A=\frac{4(b+b)}{2}\cdot4h \\ A=4\cdot4\cdot\frac{(b+B)}{2}\cdot h \\ A=16\cdot\frac{(b+B)}{2}\cdot h \end{gathered}[/tex]The area is known therefore it would remain:
[tex]\begin{gathered} A=16\cdot\frac{3}{4} \\ A=12 \end{gathered}[/tex]