$\triangle ABC \sim \triangle DEF$
When 2 triangles are similar,
then,
$\frac{Area of \triangle ABC}{Area of \triangle DEF} = \frac {AB^2}{DE^2} = \frac{BC^2}{EF^2} = \frac{AC^2}{DF^2}$
Area of $ \triangle ABC = 54cm^2$ ; BC = 3cm EF = 4cm
$\frac {54}{Area of \triangle DEF} = \frac{3^2}{4^2}$
$\frac{54}{Area of \triangle DEF} = \frac{9}{16}$
Area of $\triangle DEF = \frac{16 \times 54}{9}$
Area of $\triangle = 96cm^2$