`DeltaABC~DeltaDEF, BC=4.8cm EF=7.2cm`. Complete the following activity to find `A(DeltaABC):A(DeltaDEF)`.
Activity:
`DeltaABC~DeltaDEF`
`(A(DeltaABC))/(A(DeltaDEF))=(BC^(2))/(square^(2))`
.....Theorem on _________
`:.(A(DeltaABC))/(A(DeltaDEF))=(4.8^(2))/((square)^(2))`
`:.(A(DeltaABC))/(A(DeltaDEF))=4/(square)`
`A(DeltaABC):A(DeltaDEF)=4:square`

Explanation

To solve the problem, we need to find the ratio of the areas of triangles ABC and DEF given that they are similar triangles. We know the lengths of two corresponding sides: BC = 4.8 cm and EF = 7.2 cm.

### Step-by-Step Solution:

1. **Identify the relationship between the areas of similar triangles**:
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. This is stated as:
\[ \frac{A(\Delta ABC)}{A(\Delta DEF)} = \left(\frac{BC}{EF}\right)^2 \]

2. **Substitute the known values**:
We know that \(BC = 4.8\) cm and \(EF = 7.2\) cm. Substituting these values into the formula gives:
\[ \frac{A(\Delta ABC)}{A(\Delta DEF)} = \left(\frac{4.8}{7.2}\right)^2 \]

3. **Calculate the ratio of the sides**:
Simplifying the ratio \(\frac{4.8}{7.2}\):
\[ \frac{4.8}{7.2} = \frac{4.8 \div 4.8}{7.2 \div 4.8} = \frac{1}{1.5} = \frac{2}{3} \]

4. **Square the ratio**:
Now, we square the simplified ratio:
\[ \left(\frac{2}{3}\right)^2 = \frac{4}{9} \]

5. **Write the final ratio of the areas**:
Thus, the ratio of the areas of triangle ABC to triangle DEF is:
\[ A(\Delta ABC) : A(\Delta DEF) = 4 : 9 \]

### Final Answer:
The ratio of the areas of triangle ABC to triangle DEF is \(4 : 9\).

---