If the right triangle has the hypotenuse $a$ and the catheti $b$ and $c$, then $a^2=b^2+c^2$. Denote $A_1, A_2,A_3$ the areas of the regular nonagones with the sides $a,b,c$. All the regular nonagons are similar each to other. If two regular nonagons have the sides with the length $a$, respectively $b$, then the areas are in the ratio $\dfrac{A_1}{A_2}=\dfrac{a^2}{b^2}\Longrightarrow \dfrac{A_1}{a^2}=\dfrac{A_2}{b^2}$. Results: $\dfrac{A_1}{a^2}=\dfrac{A_2}{b^2}=\dfrac{A_3}{c^2}=\dfrac{A_2+A_3}{b^2+c^2}=\dfrac{A_2+A_3}{a^2}\Longrightarrow$ $\Longrightarrow A_1=A_2+A_3\Longrightarrow A_3=A_1-A_2=2019-1602=417 \,[\text{cm}^2]$.