# 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:

$a=3 \ \text{cm} \ \\ u=5 \ \text{cm} \ \\ \ \\ c=\sqrt{ u^2-a^2 }=\sqrt{ 5^2-3^2 }=4 \ \text{cm} \ \\ \ \\ S_{1}=a^2=3^2=9 \ \text{cm}^2 \ \\ \ \\ S_{2}=4 \cdot \ a \cdot \ c=4 \cdot \ 3 \cdot \ 4=48 \ \text{cm}^2 \ \\ \ \\ S=2 \cdot \ S_{1} + S_{2}=2 \cdot \ 9 + 48=66 \ \text{cm}^2$
$V_{1}=S_{1} \cdot \ c=9 \cdot \ 4=36 \ \text{cm}^3 \ \\ V=V_{1} \rightarrow l=V_{1} / 1000 \ l=36 / 1000 \ l=0.036 \ l=\dfrac{ 9 }{ 250 }=0.036 \ \text{l}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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