To find the area of similar figures whe you know the area of one of the figures and the length of corresponding sides:
1. Find the scale factor: in this case as you have the area of the largest figure find the scale factor for a reduction:
[tex]SF=\frac{small}{\text{big}}=\frac{9}{12}=\frac{3}{4}[/tex]2. Find the missing area: the area in similar figures is equal to the scale factor squared multiplied by the given area.
[tex]\begin{gathered} A=(\frac{3}{4})^2\cdot32in^2 \\ \\ A=(\frac{9}{16})\cdot32in^2 \\ \\ A=\frac{288}{16}in^2 \\ \\ A=18in^2 \end{gathered}[/tex]Then, the missing area is 18 square inches