Six-sided parasol

The parasol has the shape of the shell of a regular six-sided pyramid, whose base edge is a=6 dm and height v=25 cm. How much fabric is needed to make a parasol if we count 10% for joints and waste?

Final Answer:

S =  114.1724 dm²

Step-by-step explanation:

$$\begin{gathered} a=6\text{dm} \\ h=25\text{cm}\to \text{dm}=25:10\text{dm}=2.5\text{dm} \\ n=6 \\ {h}_1^2+(a/2{)}^2=a^2 \\ {h}_1=\sqrt{a^2-a^2/4}=\sqrt{6^2-6^2/4}=3\sqrt{3}\text{dm}\doteq 5.1962\text{dm} \\ {h}_2=\sqrt{h^2+h_1^2}=\sqrt{2.5^2+5.1962^2}\doteq 5.7663\text{dm} \\ {S}_1=n\cdot \frac{a\cdot h_2}{2}=6\cdot \frac{6\cdot 5.7663}{2}=9\sqrt{133}{\text{dm}}^2\doteq 103.7931{\text{dm}}^2 \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ S=q\cdot S_1=1.1\cdot 103.7931=114.1724{\text{dm}}^2 \end{gathered}$$

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