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:

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

$$\begin{gathered} V_1=S_1\cdot c=9\cdot 4=36{\text{cm}}^3 \\ V=V_1\to \text{ l}=V_1\mathrm{/}1000\text{ l}=36\mathrm{/}1000\text{ l}=0.036\text{ l}={\displaystyle \frac{9}{250}}\text{ l} \end{gathered}$$

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