Glass mosaic

How many dm² of glass is needed to produce 97 panes in the shape of a regular hexagon with a side length of 21 cm? Assume that 10% of the glass is wasted in cutting.

Final Answer:

S =  203.7528 dm²

Step-by-step explanation:

$$\begin{gathered} q=1+\frac{10}{100}=\frac{1\cdot 100}{100}+\frac{10}{100}=\frac{100}{100}+\frac{10}{100}=\frac{100+10}{100}=\frac{110}{100}=\frac{11}{10}=1.1 \\ n=97 \\ a=21\text{cm}\to \text{dm}=21:10\text{dm}=2.1\text{dm} \\ h=\sqrt{a^2-(a/2{)}^2}=\sqrt{2.1^2-(2.1/2{)}^2}\doteq 1.8187\text{dm} \\ {S}_1=\frac{a\cdot h}{2}=\frac{2.1\cdot 1.8187}{2}\doteq 1.9096{\text{dm}}^2 \\ S=n\cdot q\cdot S_1=97\cdot 1.1\cdot 1.9096=203.7528{\text{dm}}^2 \end{gathered}$$

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