In general, the volume of a triangular prism is given by the formula
[tex]\begin{gathered} V=\frac{\text{bhl}}{2} \\ b\to\text{ base of the triangular base} \\ h\to\text{ height of the triangular base} \\ l\to\text{ height of the prism} \end{gathered}[/tex]On the other hand, the surface area of such prism is
[tex]\begin{gathered} A=bh+l(s_1+s_2+s_3) \\ s_1,s_2,s_3\to\text{ sides of the triangle} \end{gathered}[/tex]Therefore, in our case,
1)
[tex]\begin{gathered} V_1=\frac{6\cdot8\cdot4}{2}=96 \\ \Rightarrow V_1=96 \\ A_1=6\cdot8+4(8+6+10) \\ \Rightarrow A_1=144 \end{gathered}[/tex]Thus, the volume and surface area of the first figure are 96ft^3 and 144ft^2, respectively.
2) Similarly
[tex]V_2=\frac{11\cdot3.9\cdot12}{2}=257.4[/tex]In this prism, the dotted line marks the height of the triangular base.
Thus,
[tex]A_2=11\cdot3.9+12(4+11+11)=354.9[/tex]The volume and surface area of the second figure are 257.4ft^3 and 354.9ft^2, respectively.
3) Once again, the dotted line indicates the height of the triangular base; thus,
[tex]\begin{gathered} V_3=\frac{12\cdot3.6\cdot10}{2}=216 \\ \Rightarrow V_3=216 \\ \text{and} \\ A_3=12\cdot3.6+10(6+8+12)=303.2 \end{gathered}[/tex]The volume and surface area of the third figure are 216ft^3 and 303.2ft^2, respectively.
