# Glass mosaic

How many dm2 glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%.

Result

S =  203.753 dm2

#### Solution:

$q=1 + \dfrac{ 10 }{ 100 }=\dfrac{ 11 }{ 10 }=1.1 \ \\ n=97 \ \\ a=21 \ cm \rightarrow dm=21 / 10 \ dm=2.1 \ dm \ \\ \ \\ h=\sqrt{ a^{ 2 }-(a/2)^{ 2 } }=\sqrt{ 2.1^{ 2 }-(2.1/2)^{ 2 } } \doteq 1.8187 \ \text{dm} \ \\ \ \\ S_{1}=\dfrac{ a \cdot \ h }{ 2 }=\dfrac{ 2.1 \cdot \ 1.8187 }{ 2 } \doteq 1.9096 \ \text{dm}^2 \ \\ \ \\ S=n \cdot \ q \cdot \ S_{1}=97 \cdot \ 1.1 \cdot \ 1.9096 \doteq 203.7528 \doteq 203.753 \ \text{dm}^2$

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