To get the surface area of the figure
we will follow the steps below
Step 1: Find the surface area of the pyramid excluding its base
The pyramid has four triangles: 2 triangles are similar while the other two are also similar (They have the same dimensions)
[tex]\begin{gathered} \Rightarrow \\ 2(\frac{1}{2}\times3\times8)+2(\frac{1}{2}\times4\times\sqrt[]{21}) \end{gathered}[/tex]
=>
[tex]24+4\sqrt[]{21}[/tex]
=>
[tex]42.33[/tex]
Step 2: Find the surface area of the cuboid excluding its surface
The surface area of the cuboid will be
[tex]8\times4+2(3\times4)+2(8\times3)[/tex]
=>
[tex]104[/tex]
Total surface area =42.33+ 104 =146.33 square units
Total surface area=146.33 square units
To get the volume
we will have to find the volume of the pyramid and that of the cuboid
To get The volume of the pyramid, we will have to get its height
Then we can then get the height
[tex]\begin{gathered} \text{height}^2=(\sqrt[]{21})^2-4^2 \\ \text{height}=\sqrt[]{5} \end{gathered}[/tex]
The volume of the pyramid will be
[tex]\begin{gathered} V=\frac{1}{3}\times base\text{ area}\times height \\ V=\frac{1}{3}\times3\times8\times\sqrt[]{5} \\ V=8\sqrt[]{5} \\ V=17.89 \end{gathered}[/tex]
The volume of the cuboid
=>
lxbxh= 8x4x3=96
The volume of the cuboid will be =17.89+96 =113.89 cubic units
