Pyramid roof

1/3 of the area of ​​the roof-shaped regular tetrahedral pyramid with base edge 8 m and height of 4 m is already covered with roofing. How many square meters still need to be covered?

Correct answer:

S =  60.3398 m²

Step-by-step explanation:

$$\begin{gathered} a=8\text{m} \\ h=4\text{m} \\ q=1-1/3=\frac{2}{3}\doteq 0.6667 \\ {h}_1=\sqrt{h^2+(a/2{)}^2}=\sqrt{4^2+(8/2{)}^2}=4\sqrt{2}\text{m}\doteq 5.6569\text{m} \\ {S}_1=\frac{a\cdot h_1}{2}=\frac{8\cdot 5.6569}{2}=16\sqrt{2}{\text{m}}^2\doteq 22.6274{\text{m}}^2 \\ S=q\cdot 4\cdot S_1=0.6667\cdot 4\cdot 22.6274=60.3398{\text{m}}^2 \end{gathered}$$

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