Tent fabric calculation

The children's tent with a beech wood floor has the shape of a regular four-sided pyramid with a base edge of 1.25 m and a height of 80 cm. How many m² of fabric do we need to finish the tent if we add 12% material to the folds?

Final Answer:

S =  4.5926 m²

Step-by-step explanation:

$$\begin{gathered} a=1.25\text{m} \\ h=80\text{cm}\to \text{m}=80:100\text{m}=0.8\text{m}\text{m} \\ s=\sqrt{h^2+(a/2{)}^2}=\sqrt{0.8^2+(1.25/2{)}^2}\doteq 1.0152\text{m} \\ {S}_1=a\cdot s/2=1.25\cdot 1.0152/2\doteq 0.6345{\text{m}}^2 \\ q=100\%+12\%=1+\frac{12}{100}=1.12 \\ {S}_0=a^2+4\cdot S_1=1.25^2+4\cdot 0.6345\doteq 4.1005{\text{m}}^2 \\ S=q\cdot S_0=1.12\cdot 4.1005=4.5926{\text{m}}^2 \end{gathered}$$

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