The given solid is composed of a rectangular prism and a rectangular pyramid.
The surface area of a prism is
[tex]\begin{gathered} S_{\text{prism}}=2lw+2wh+2lh=2\cdot4\cdot8+2\cdot8\cdot3+2\cdot4\cdot3_{} \\ S_{\text{prism}}=64+48+24=136u^2 \end{gathered}[/tex]
The surface area of a rectangular pyramid is
[tex]S_{\text{pyramid}}=A+\frac{1}{2}ps[/tex]
But we'll not include the area of base A because it's already included in the surface area of the prism. p is the perimeter, and s is the slant height.
[tex]\begin{gathered} S_{pyramid}=\frac{1}{2}\cdot(8+4+8+4)\cdot\sqrt[]{21}=\frac{1}{2}\cdot24\cdot\sqrt[]{21} \\ S_{\text{pyramid}}=12\sqrt[]{21}u^2\approx55 \end{gathered}[/tex]
Then, we find the volumes. The volume of the prism is
[tex]V_{\text{prism}}=w\cdot l\cdot h=8\cdot4\cdot3=96u^3[/tex]
The volume of the pyramid is
[tex]V_{\text{pyramid}}=\frac{1}{3}\cdot(w\cdot l)\cdot(h_1)[/tex]
Then, the volume is
[tex]V_{\text{pyramid}}=\frac{1}{3}\cdot8\cdot4\cdot(\sqrt[]{21-16})=\frac{32}{3}\cdot\sqrt[]{5}[/tex]
