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)

Correct result:

V =  312.8 dm³
S =  496.4 dm²

Solution:

$$\begin{gathered} a=6.8\text{ dm } \\ {v}_1=4\text{ dm } \\ {v}_2=23\text{ dm } \\ {S}_1=a\cdot v_1\mathrm{/}2=6.8\cdot 4\mathrm{/}2={\displaystyle \frac{68}{5}}=13.6{\text{dm}}^2 \\ V=S_1\cdot v_2=13.6\cdot 23={\displaystyle \frac{1564}{5}}={\displaystyle \frac{1564}{5}}{\text{dm}}^3=312.8{\text{dm}}^3 \end{gathered}$$

$$\begin{gathered} S_2=(a+a+a)\cdot v_2=(6.8+6.8+6.8)\cdot 23={\displaystyle \frac{2346}{5}}=469.2{\text{dm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 13.6+469.2={\displaystyle \frac{2482}{5}}={\displaystyle \frac{2482}{5}}{\text{dm}}^2=496.4{\text{dm}}^2 \end{gathered}$$

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