Four-sided turret

The turret has the shape of a regular four-sided pyramid with a base edge 0.8 m long. The height of the turret is 1.2 m. How many square meters are needed to cover it, counting the extra 10% sheet metal waste?

Final Answer:

S =  2.2262 m²

Step-by-step explanation:

$$\begin{gathered} a=0.8\text{m} \\ h=1.2\text{m} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{1.2^2+(0.8/2{)}^2}\doteq 1.2649\text{m} \\ {S}_1=\frac{a\cdot h_2}{2}=\frac{0.8\cdot 1.2649}{2}\doteq 0.506{\text{m}}^2 \\ {S}_2=4\cdot S_1=4\cdot 0.506\doteq 2.0239{\text{m}}^2 \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ S=S_2\cdot q=2.0239\cdot 1.1=2.2262{\text{m}}^2 \end{gathered}$$

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