Triangular prism

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

Correct answer:

V =  312.8 dm³
S =  496.4 dm²

Step-by-step explanation:

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

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

Try another example