# 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.

Result

S =  189.9 m2

#### Solution:

$a = 12 \ m \ \\ v = 4.5 \ m \ \\ q = 1 + \dfrac{ 5.5 }{ 100 } = \dfrac{ 211 }{ 200 } = 1.055 \ \\ \ \\ h_{ 2 } = \sqrt{ v^2 + (a/2)^2 } = \sqrt{ 4.5^2 + (12/2)^2 } = \dfrac{ 15 }{ 2 } = 7.5 \ m \ \\ \ \\ S_{ 1 } = a \cdot \ h_{ 2 } /2 = 12 \cdot \ 7.5 /2 = 45 \ m^2 \ \\ \ \\ S_{ 2 } = 4 \cdot \ S_{ 1 } = 4 \cdot \ 45 = 180 \ m^2 \ \\ S = S_{ 2 } \cdot \ q = 180 \cdot \ 1.055 = \dfrac{ 1899 }{ 10 } = 189.9 = 189.9 \ m^2$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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