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 cm u=5 cm  c=u2a2=5232=4 cm  S1=a2=32=9 cm2  S2=4 a c=4 3 4=48 cm2  S=2 S1+S2=2 9+48=66 cm2a=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
V1=S1 c=9 4=36 cm3 V=V1l=V1/1000 l=36/1000 l=0.036 l=9250=0.036 lV_{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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