Tetrahedral prism

Calculate the surface and volume of a tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are a = 12 cm, b = 7 cm, ha = 6 cm, and prism height h = 10 cm.

Correct answer:

S =  524 cm²
V =  720 cm³

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm} \\ b=7\text{cm} \\ v=6\text{cm} \\ h=10\text{cm} \\ {S}_1=a\cdot v=12\cdot 6=72{\text{cm}}^2 \\ {S}_2=h\cdot (2\cdot a+2\cdot b)=10\cdot (2\cdot 12+2\cdot 7)=380{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 72+380=524{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot h=72\cdot 10=720{\text{cm}}^3$

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