Tetrahedral prism - rhomboid base

Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are:
a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.

Correct answer:

S =  5.24 dm²
V =  0.72 dm³

Step-by-step explanation:

$$\begin{gathered} a=12\mathrm{/}10={\displaystyle \frac{6}{5}}=1.2 \\ b=70\mathrm{/}100={\displaystyle \frac{7}{10}}=0.7 \\ v=6\mathrm{/}10={\displaystyle \frac{3}{5}}=0.6 \\ h=1 \\ {S}_1=a\cdot v=1.2\cdot 0.6={\displaystyle \frac{18}{25}}=0.72 \\ {S}_2=2\cdot (a+b)\cdot h=2\cdot (1.2+0.7)\cdot 1={\displaystyle \frac{19}{5}}=3.8 \\ S=2\cdot S_1+S_2=2\cdot 0.72+3.8={\displaystyle \frac{131}{25}}={\displaystyle \frac{131}{25}}{\text{dm}}^2=5.24{\text{dm}}^2 \end{gathered}$$

$V=S_1\cdot h=0.72\cdot 1={\displaystyle \frac{18}{25}}={\displaystyle \frac{18}{25}}{\text{dm}}^3=0.72{\text{dm}}^3$

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