Triangular prism

Calculate the volume and surface area of a triangular prism if it is given:
a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height)

Result

V =  312.8 dm³
S =  496.4 dm²

Solution:

$a=6.8 \ \text{dm} \ \\ v_{1}=4 \ \text{dm} \ \\ v_{2}=23 \ \text{dm} \ \\ S_{1}=a \cdot \ v_{1} / 2=6.8 \cdot \ 4 / 2=\dfrac{ 68 }{ 5 }=13.6 \ \\ V=S_{1} \cdot \ v_{2}=13.6 \cdot \ 23=\dfrac{ 1564 }{ 5 }=312.8 \ \text{dm}^3$

$S_{2}=(a+a+a) \cdot \ v_{2}=(6.8+6.8+6.8) \cdot \ 23=\dfrac{ 2346 }{ 5 }=469.2 \ \\ S=2 \cdot \ S_{1} + S_{2}=2 \cdot \ 13.6 + 469.2=\dfrac{ 2482 }{ 5 }=496.4 \ \text{dm}^2$

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