Regular prism

The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.

Result

V =  200 cm2

Solution:

S1=25 cm2 S=210 cm2  a=S1=25=5 cm  S=2⋅ S1+4av  v=(S−2⋅ S1)/(4⋅ a)=(210−2⋅ 25)/(4⋅ 5)=8 cm  V=S1⋅ v=25⋅ 8=200 cm2S_{1}=25 \ \text{cm}^2 \ \\ S=210 \ \text{cm}^2 \ \\ \ \\ a=\sqrt{ S_{1} }=\sqrt{ 25 }=5 \ \text{cm} \ \\ \ \\ S=2 \cdot \ S_{1} + 4av \ \\ \ \\ v=(S-2 \cdot \ S_{1} )/ (4 \cdot \ a)=(210-2 \cdot \ 25 )/ (4 \cdot \ 5)=8 \ \text{cm} \ \\ \ \\ V=S_{1} \cdot \ v=25 \cdot \ 8=200 \ \text{cm}^2

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