Answer
$Ma_{2}=25.2$ cm$^{2}$
Work Step by Step
The flow is assumed to be isentropic, and thus the stagnation and critical properties remain constant throughout the nozzle. The flow area at a location where $\mathrm{Ma}_2=0.9$ is determined using $A / A^*$ data from Table $\mathrm{A}-32$ to be $$
\begin{aligned}
& \mathrm{Ma}_1=1.8: \quad \frac{A_1}{A^*}=1.4390 \longrightarrow A^*=\frac{A_1}{1.4390}=\frac{36 \mathrm{~cm}^2}{1.4390}=25.02 \mathrm{~cm}^2 \\
& \mathrm{Ma}_2=0.9: \quad \frac{A_2}{A^*}=1.0089 \longrightarrow A_2=(1.0089) A^*=(1.0089)\left(25.02 \mathrm{~cm}^2\right)=\mathbf{2 5 . 2} \mathbf{c m}^2
\end{aligned}
$$
