Given: 1) $\text{Area of $\triangle$ ABC =7 cm$^{2}$}$
2) $EC=3BE$
We know that area of triangle =$\frac{1}{2}*B*H$
so Area of $\triangle$ ABE $= \frac{1}{2}*B*H$
$\implies 7=\frac{1}{2}*B*H$
$\implies B*H=14 $
This can be also written as $ \text{ BE*AB=14 cm $^{2}$}\cdots\cdots(i)$
Now area of rectangle $ABCD= AB*BC$
$\implies AB* (4*BE)$
$\implies 4*14=56 $ sq cm
Note: $(BC=BE+EC\implies BE+3BE=4BE)$
Option $(D)$ is correct.