Roof cover

Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m2 of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste.

Correct result:

S =  189.9 m2

Solution:

a=12 m v=4.5 m q=1+5.5100=211200=1.055  h2=v2+(a/2)2=4.52+(12/2)2=152=7.5 m  S1=a⋅ h2/2=12⋅ 7.5/2=45 m2  S2=4⋅ S1=4⋅ 45=180 m2 S=S2⋅ q=180⋅ 1.055=189910=189.9 m2a=12 \ \text{m} \ \\ v=4.5 \ \text{m} \ \\ q=1 + \dfrac{ 5.5 }{ 100 }=\dfrac{ 211 }{ 200 }=1.055 \ \\ \ \\ h_{2}=\sqrt{ v^2 + (a/2)^2 }=\sqrt{ 4.5^2 + (12/2)^2 }=\dfrac{ 15 }{ 2 }=7.5 \ \text{m} \ \\ \ \\ S_{1}=a \cdot \ h_{2} /2=12 \cdot \ 7.5 /2=45 \ \text{m}^2 \ \\ \ \\ S_{2}=4 \cdot \ S_{1}=4 \cdot \ 45=180 \ \text{m}^2 \ \\ S=S_{2} \cdot \ q=180 \cdot \ 1.055=\dfrac{ 1899 }{ 10 }=189.9 \ \text{m}^2

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