Example Tutor 3. Find the height of the triangular prism. \[ \begin{aligned} \boldsymbol{V} & =\boldsymbol{B} \boldsymbol{h} & & \text { Volume of a triangular prism } \\ \boldsymbol{V} & =\left(\frac{1}{\mathbf{2}} \cdot \mathbf{1} \cdot \mathbf{0 . 3}\right) \boldsymbol{h} & & \text { Replace } B \text { with } \frac{1}{2} \cdot 1 \cdot 0.3 . \\ \mathbf{1 2} & =\left(\frac{1}{2} \cdot 1 \cdot 0.3\right) h & & \text { Replace } V \text { with } 12 . \\ 12 & =0.15 h & & \text { Multiply. } \\ \frac{12}{\mathbf{0 . 1 5}} & =\frac{0.15 h}{\mathbf{0 . 1 5}} & & \text { Divide each side by } 0.15 . \\ 80 & =h & & \text { Simplify. } \end{aligned} \] So, the height of the prism is 80 cm . Got 1t? Do this problem to find out. Find the missing dimension of the triangular prism. d. \( V=55 \mathrm{~km}^{3} \), base length \( =2 \mathrm{~km} \), base height \( =5 \mathrm{~km}, h= \) ?
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Bonus Knowledge
Did you know that the triangular prism has been used for centuries in various fields like architecture and engineering? The ancient Greeks utilized triangular shapes in their structures for added strength and stability. This design philosophy continues today, with countless buildings using triangular prisms to not only create eye-catching aesthetics but also maximize internal space and support structural integrity! When tackling this problem, it's essential to remember that volume equals area of the base times height! A common mistake is forgetting to convert units if working in different scales, so make sure every component is consistent—whether you're using kilometers, meters, or any other unit. Before diving into calculations, verify that all measurements align with the same measurement system to avoid errors!
