Dimensions 6578

How many m² of fabric is needed to make a tent of a regular 3-sided prism if it is necessary to count on a 2% reserve of fabric? Dimensions - 2m 1.6m and height 1.4m

Correct answer:

S =  8.4716 m²

Step-by-step explanation:

$$\begin{gathered} a=2\text{m} \\ b=1.6\text{m} \\ h=1.4\text{m} \\ p=1+\frac{2}{100}=\frac{1\cdot 100}{100}+\frac{2}{100}=\frac{100}{100}+\frac{2}{100}=\frac{100+2}{100}=\frac{102}{100}=\frac{51}{50}=1.02 \\ {S}_1=a\cdot h/2=2\cdot 1.4/2=\frac{7}{5}=1.4{\text{m}}^2 \\ s=\sqrt{h^2+(a/2{)}^2}=\sqrt{1.4^2+(2/2{)}^2}\doteq 1.7205\text{m} \\ {S}_2=b\cdot s=1.6\cdot 1.7205\doteq 2.7527{\text{m}}^2 \\ S=p\cdot (2\cdot S_1+2\cdot S_2)=1.02\cdot (2\cdot 1.4+2\cdot 2.7527)=8.4716{\text{m}}^2 \end{gathered}$$

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