The Scout Tent

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

Correct answer:

x =  7.1251 m²

Step-by-step explanation:

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

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