Quadrilateral shelter

The shelter has the shape of a regular quadrilateral pyramid without a front wall. The length of the base edge is 3 meters, and the shelter's height is 3.5 meters. How much canvas must be bought to sew it if we have to increase consumption by 20% for folds and cuts?

Final Answer:

S =  20.5626 m²

Step-by-step explanation:

$$\begin{gathered} n=4-1=3 \\ a=3\text{m} \\ h=3.5\text{m} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{3.5^2+(3/2{)}^2}\doteq 3.8079\text{m} \\ {S}_1=\frac{h_2\cdot a}{2}=\frac{3.8079\cdot 3}{2}\doteq 5.7118{\text{m}}^2 \\ q=100\%+20\%=1+\frac{20}{100}=1.2 \\ S=n\cdot q\cdot S_1=3\cdot 1.2\cdot 5.7118=20.5626{\text{m}}^2 \end{gathered}$$

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