Tetrahedral pyramid

Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm², and the deviation angle of the side edges from the plane of the base is 60 degrees.

Correct answer:

V =  36.51 cm³
S =  72.915 cm²

Step-by-step explanation:

$$\begin{gathered} b=\sqrt{h^2+(a/2{)}^2}=\sqrt{5.4772^2+(4.4721/2{)}^2}=\sqrt{35}\text{cm}\doteq 5.9161\text{cm} \\ {S}_2=a\cdot b/2=4.4721\cdot 5.9161/2=5\sqrt{7}{\text{cm}}^2\doteq 13.2288{\text{cm}}^2 \\ S=4\cdot S_2+S_1=4\cdot 13.2288+20=72.915{\text{cm}}^2 \end{gathered}$$

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