Tetrahedral prism

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

Final Answer:

S =  5.24 dm²
V =  0.72 dm³

Step-by-step explanation:

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

$V=S_1\cdot h=0.72\cdot 1=0.72{\text{dm}}^3$

Try another example