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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UpStudy AI · Accepted Answer

$$
\begin{aligned}
\text{Area of the triangular base, } B & = \frac{1}{2} \times \text{base length} \times \text{base height} \
& = \frac{1}{2} \times 2\,\text{km} \times 5\,\text{km} \
& = 5\,\text{km}^2.
\end{aligned}
$$

$$
\begin{aligned}
\text{Volume of the prism, } V & = B \times h \
55\,\text{km}^3 & = 5\,\text{km}^2 \times h.
\end{aligned}
$$

$$
\begin{aligned}
h & = \frac{55\,\text{km}^3}{5\,\text{km}^2} \
& = 11\,\text{km}.
\end{aligned}
$$

Thus, the missing height of the prism is $$11\,\text{km}$$.
The height of the prism is 11 km.

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