Perimeter of needle

The perimeter of the four-sided needle is 48 m, and its height is 2.5 m; how much will the sheet metal for this pyramid cost? If 1 m² costs €1.5, a 12% loss due to joints and folds is included in the area.

Final Answer:

x =  504 eur

Step-by-step explanation:

$$\begin{gathered} o=48\text{m} \\ h=2.5\text{m} \\ r=100\%+12\%=1+\frac{12}{100}=1.12 \\ o=4a \\ a=o/4=48/4=12\text{m} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{2.5^2+(12/2{)}^2}=\frac{13}{2}=6.5\text{m} \\ {S}_1=a^2+4\cdot \frac{a\cdot h_2}{2}=12^2+4\cdot \frac{12\cdot 6.5}{2}=300{\text{m}}^2 \\ {S}_2=r\cdot S_1=1.12\cdot 300=336{\text{m}}^2 \\ x=1.5\cdot S_2=1.5\cdot 336=504\text{eur} \end{gathered}$$

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