If ABCD  is a rectangle whose area is $108 m^2$ and length is $12 m$, then the area of the square AEFC is

ABCD  is a rectangle

Given Area of rectangle $=108m{t}^2$ and $AB=12mts$

$\begin{array}{l}AB\times BC=108m^2\\ 12\times BC=108\\ BC=\frac{108}{12}\\ BC=9m\\ Also,AD=9m,CD=AB=12m\\ \overline{)ADC}=90°\left(\text{angle in a rectangle}\right)\end{array}$

In right angled triangle ADC

$\begin{array}{l}A{C}^2=A{D}^2+D{C}^2\\ ={\left(9\right)}^2+{\left(12\right)}^2\\ =81+144=225\\ AC=\sqrt{225}=15m\end{array}$

$\therefore$area of square $ACFE={\left(AC\right)}^2$

$={\left(15\right)}^2$

$=225m^2$