State the Geometric Property

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

$\frac{\text{Area}_{\text{small}}}{\text{Area}_{\text{big}}} = \left(\frac{\text{Side}_{\text{small}}}{\text{Side}_{\text{big}}}\right)^2$

Substitute Given Values

Substitute the ratio $3/4$ and the area of the smaller triangle into the formula.

$\frac{54}{\text{Area}_{\text{big}}} = \left(\frac{3}{4}\right)^2 = \frac{9}{16}$

Calculate the Area

Cross-multiply to solve for the area of the bigger triangle: $\text{Area}_{\text{big}} = 54 \times \frac{16}{9}$.

$\text{Area}_{\text{big}} = 6 \times 16 = 96$