Pyramid-shaped roof

A block-shaped shed is covered with a quadrilateral pyramid-shaped roof with a base with sides of 6m and 3m and a height of 2.5m. How many m² (square meters) must be purchased if an extra 40% is calculated for roofing and waste?

Correct answer:

S =  40.8915 m²

Step-by-step explanation:

$$\begin{gathered} a=6\text{m} \\ b=3\text{m} \\ h=2.5\text{m} \\ q=1+\frac{40}{100}=\frac{1\cdot 100}{100}+\frac{40}{100}=\frac{100}{100}+\frac{40}{100}=\frac{100+40}{100}=\frac{140}{100}=\frac{7}{5}=1.4 \\ {h}_1=\sqrt{h^2+(a/2{)}^2}=\sqrt{2.5^2+(6/2{)}^2}\doteq 3.9051\text{m} \\ {h}_2=\sqrt{h^2+(b/2{)}^2}=\sqrt{2.5^2+(3/2{)}^2}\doteq 2.9155\text{m} \\ {S}_1=\frac{b\cdot h_1}{2}=\frac{3\cdot 3.9051}{2}\doteq 5.8577{\text{m}}^2 \\ {S}_2=\frac{a\cdot h_2}{2}=\frac{6\cdot 2.9155}{2}\doteq 8.7464{\text{m}}^2 \\ S=q\cdot (2\cdot S_1+2\cdot S_2)=1.4\cdot (2\cdot 5.8577+2\cdot 8.7464){\text{m}}^2=40.8915{\text{m}}^2 \end{gathered}$$

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