Prism 4 sides

The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters

Correct result:

S =  66 cm²
V =  0.036 l

Solution:

$$\begin{gathered} a=3\text{ cm } \\ u=5\text{ cm } \\ c=\sqrt{u^2-a^2}=\sqrt{5^2-3^2}=4\text{ cm } \\ {S}_1=a^2=3^2=9{\text{cm}}^2 \\ {S}_2=4\cdot a\cdot c=4\cdot 3\cdot 4=48{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 9+48=66{\text{cm}}^2 \end{gathered}$$

$V_{1}=S_{1} \cdot \ c=9 \cdot \ 4=36 \ \text{cm}^3 \ \\ V=V_{1} \rightarrow l=V_{1} / 1000 \ l=36 / 1000 \ l=0.036 \ l=\dfrac{ 9 }{ 250 }=0.036 \ \text{l}$

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