Question

I'm doing surface area and volume of triangular prisms. I understand that i have to do a= bh+ l (s^1+s^2+s^3) is what my teacher taught me. but im so confused on which numbers are base or height or length, and its different shaped triangular prisms, which is even more confusing. Please help me.

Answer 1

In general, the volume of a triangular prism is given by the formula

`\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}`

On the other hand, the surface area of such prism is

`\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}`

Therefore, in our case,

1)

`\begin{gathered} V_1=(6\cdot8\cdot4)/(2)=96 \\ \Rightarrow V_1=96 \\ A_1=6\cdot8+4(8+6+10) \\ \Rightarrow A_1=144 \end{gathered}`

Thus, the volume and surface area of the first figure are 96ft^3 and 144ft^2, respectively.

2) Similarly

`V_2=(11\cdot3.9\cdot12)/(2)=257.4`

In this prism, the dotted line marks the height of the triangular base.

Thus,

`A_2=11\cdot3.9+12(4+11+11)=354.9`

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,

`\begin{gathered} V_3=(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}`

The volume and surface area of the third figure are 216ft^3 and 303.2ft^2, respectively.