Suppose that the dilation coefficient between two 2D figures is equal to k; therefore, the ratio between their corresponding sides is k. On the other hand, the ratio between the area of the two shapes is equal to k^2.
Therefore, in our case, the dilation coefficient is
[tex]\frac{6}{3}=2=k\to\text{ dilation coefficient}[/tex]
Then, as for the area,
[tex]24=k^2A[/tex]
Where A is the area of the smaller figure.
Thus,
[tex]\begin{gathered} \Rightarrow\frac{24}{k^2}=A \\ \Rightarrow A=\frac{24}{2^2}=\frac{24}{4}=6 \\ \Rightarrow A=6 \end{gathered}[/tex]
Therefore, the answer is 6in^2
