The Scout Tent

The Scout Tent has a rectangular wooden underlay with dimensions of 220 cm and 150 cm. How much canvas is needed for a 170 cm high pyramid roof?

Correct answer:

x =  7.1251 m²

Step-by-step explanation:

$$\begin{gathered} a=220\text{ cm}\to \text{ m}=220\mathrm{/}100\text{ m}=2.2\text{ m } \\ b=150\text{ cm}\to \text{ m}=150\mathrm{/}100\text{ m}=1.5\text{ m } \\ h=170\text{ cm}\to \text{ m}=170\mathrm{/}100\text{ m}=1.7\text{ m } \\ {h}_1=\sqrt{h^2+(b\mathrm{/}2{)}^2}=\sqrt{1.7^2+(1.5\mathrm{/}2{)}^2}\doteq 1.8581\text{ m } \\ {h}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{1.7^2+(2.2\mathrm{/}2{)}^2}\doteq 2.0248\text{ m } \\ {S}_1=a\cdot h_1\mathrm{/}2=2.2\cdot 1.8581\mathrm{/}2\doteq 2.0439{\text{m}}^2 \\ {S}_2=b\cdot h_2\mathrm{/}2=1.5\cdot 2.0248\mathrm{/}2\doteq 1.5186{\text{m}}^2 \\ x=2\cdot (S_1+S_2)=2\cdot (2.0439+1.5186)=7.1251{\text{m}}^2 \end{gathered}$$

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