# 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

Result

S =  66 cm2
V =  0.036 l

#### Solution:

$a=3 \ \text{cm} \ \\ u=5 \ \text{cm} \ \\ \ \\ c=\sqrt{ u^2-a^2 }=\sqrt{ 5^2-3^2 }=4 \ \text{cm} \ \\ \ \\ S_{1}=a^2=3^2=9 \ \text{cm}^2 \ \\ \ \\ S_{2}=4 \cdot \ a \cdot \ c=4 \cdot \ 3 \cdot \ 4=48 \ \text{cm}^2 \ \\ \ \\ S=2 \cdot \ S_{1} + S_{2}=2 \cdot \ 9 + 48=66 \ \text{cm}^2$
$V_{1}=S_{1} \cdot \ c=9 \cdot \ 4=36 \ \text{cm}^3 \ \\ V=V_{1} \rightarrow l=V_{1} / 1000 \ l=36 / 1000 \ l=0.036 \ l=\dfrac{ 9 }{ 250 }=0.036 \ \text{l}$

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