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 answer:

S =  66 cm²
V =  0.036 l

Step-by-step explanation:

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

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

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