Prism height

What is the height of a prism with a right triangle base and sides of 6 cm and 9 cm? The hypotenuse is 10.8 cm long. The volume of the prism is 58 cm³. Calculate its surface area.

Correct answer:

h =  2.1481 cm
S =  109.4222 cm²

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ b=9\text{cm} \\ c=10.8\text{cm} \\ V=58{\text{cm}}^3 \\ {S}_1=\frac{a\cdot b}{2}=\frac{6\cdot 9}{2}=27{\text{cm}}^2 \\ V=S_1\cdot h \\ h=V/S_1=58/27=\frac{58}{27}\text{cm}=2.1481\text{cm} \end{gathered}$$

$$\begin{gathered} S_2=(a+b+c)\cdot h=(6+9+10.8)\cdot 2.1481=\frac{2494}{45}\doteq 55.4222{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 27+\frac{2494}{45}=109.4222{\text{cm}}^2 \end{gathered}$$

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