Here, we are given a triangular prism.
Given:
Volume, V = 162 cubic meters
Height, h = 9 meters
Length, l = 6 meters
Base, b = ?
To find the base, b, of the triangular prism, use the formula for the volume of a triangular prism below:
[tex]\begin{gathered} V=\frac{1}{2}\ast base\ast height\ast length \\ \\ V=\frac{1}{2}bhl \end{gathered}[/tex]
Rewrite the formula for b:
[tex]\begin{gathered} V=\frac{1}{2}\text{bhl} \\ \\ \text{Multiply both sides by 2:} \\ 2V=\frac{\text{bhl}}{2}\ast2 \\ \\ 2V=\text{bhl} \\ \\ \text{Divide both sides by hl:} \\ \frac{2V}{hl}=\frac{\text{bhl}}{hl} \\ \\ \frac{2V}{hl}=b \\ \\ b=\frac{2V}{hl} \end{gathered}[/tex]
Now, input values into the equation:
[tex]\begin{gathered} b=\frac{2V}{hl} \\ \\ b=\frac{2\ast162}{9\ast6} \\ \\ b=\frac{324}{54} \\ \\ b=6\text{ meters} \end{gathered}[/tex]
Therefore, the value of b is 6
ANSWER:
6 m
