Let [tex]V_s[/tex] be the volume of the solid S. We can write:
[tex]V_{shaded} = V_{triangular} - V_{rectangular}[/tex]
Now, we just need to calculate the volume of the original prism (Vtriangular) and the volume that was removed (Vrectangular). So:
[tex]\bullet ~V_{triangular} = S_{\triangle basis}\times h\\\\
V_{triangular} = \dfrac{5\times5.7}{2}\times4\\\\
V_{triangular} = 57~u^3\\\\\\
\bullet ~V_{rectangular} = S_{\square basis}\times h\\\\
V_{rectangular} = 1.7^2\times4\\\\
V_{rectangular} = 11.56~u^3[/tex]
Then,
[tex]V_{shaded} = V_{triangular} - V_{rectangular}\\\\
V_{shaded} = 57 - 11.56\\\\
V_{shaded} = 45.44~u^3\\\\
\boxed{V_{shaded} \approx 45.4~u^3}[/tex]
Thus, the answer is 45.4 u³.
