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 of pyramid roof?

Correct result:

x =  7.125 m2

Solution:

a=220 cmm=220/100 m=2.2 m b=150 cmm=150/100 m=1.5 m h=170 cmm=170/100 m=1.7 m  h1=h2+(b/2)2=1.72+(1.5/2)21.8581 m h2=h2+(a/2)2=1.72+(2.2/2)22.0248 m  S1=a h1/2=2.2 1.8581/22.0439 m2 S2=b h2/2=1.5 2.0248/21.5186 m2  x=2 (S1+S2)=2 (2.0439+1.5186)=7.125 m2a=220 \ cm \rightarrow m=220 / 100 \ m=2.2 \ m \ \\ b=150 \ cm \rightarrow m=150 / 100 \ m=1.5 \ m \ \\ h=170 \ cm \rightarrow m=170 / 100 \ m=1.7 \ 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)=7.125 \ \text{m}^2



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