Roof 7

The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?

Result

p =  4.815 %

Solution:

a=12 m h=4 m S=181.4 m2 h2=h2+(a/2)2=42+(12/2)22 13 m7.2111 m S1=h2 a/2=7.2111 12/212 13 m243.2666 m2 S2=4 S1=4 43.266648 13 m2173.0665 m2 p=100 (SS2)/S2=100 (181.4173.0665)/173.06654.81524.815%a=12 \ \text{m} \ \\ h=4 \ \text{m} \ \\ S=181.4 \ \text{m}^2 \ \\ h_{2}=\sqrt{ h^2 + (a/2)^2 }=\sqrt{ 4^2 + (12/2)^2 } \doteq 2 \ \sqrt{ 13 } \ \text{m} \doteq 7.2111 \ \text{m} \ \\ S_{1}=h_{2} \cdot \ a /2=7.2111 \cdot \ 12 /2 \doteq 12 \ \sqrt{ 13 } \ \text{m}^2 \doteq 43.2666 \ \text{m}^2 \ \\ S_{2}=4 \cdot \ S_{1}=4 \cdot \ 43.2666 \doteq 48 \ \sqrt{ 13 } \ \text{m}^2 \doteq 173.0665 \ \text{m}^2 \ \\ p=100 \cdot \ (S-S_{2})/S_{2}=100 \cdot \ (181.4-173.0665)/173.0665 \doteq 4.8152 \doteq 4.815 \%



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