If $$\triangle$$ ABC is similar to $$\triangle$$ DEF such that BC= 3 cm, EF = 4 cm and the area of $$\triangle ABC= 54 cm^{2}$$, then the area of $$\triangle$$ DEF is:

If $$\triangle$$ ABC is similar $$\triangle$$ DEF such that BC= 3 cm, EF = 4 cm.

Area of $$\triangle ABC = 54 cm^{2}$$

$$\frac{1}{2}\times\ base\ of\ triangle\ ABC \times\ height\ of\ triangle\ ABC=54$$

$$\frac{1}{2}\times\ 3\times\ height\ of\ triangle\ ABC=54$$

$$\frac{1}{2}\times\ height\ of\ triangle\ ABC=18$$

height of triangle ABC = 36 cm

As we know that in similar triangles, their corresponding sides are in the same proportion.

So BC : EF = 3 : 4

Similarly, height of triangle ABC : height of triangle DEF = 36 : $$\frac{36}{3}\times\ 4$$ = 36 : 48

Area of $$\triangle$$ DEF = $$\frac{1}{2}\times base\ of\ triangle\ DEF\times height\ of\ triangle\ DEF$$

= $$\frac{1}{2}\times\ 4\times\ 48$$

= $$2\times48$$

= 96 $$cm^{2}$$