Find the length $ l $ of a triangular prism if side $a = 6$ and area $A = 229.2$.

$l = 11.0013$

To find length $ l $ use formula:

$$ A = \frac{ a^2 \sqrt{3}}{2} + 3 a l $$

After substituting $ A = 229.2 $ and $ a = 6 $ we have:

$$ 229.2 = \frac{ 6^2 \sqrt{3}}{2} + 3 \cdot 6 \cdot l $$$$ 229.2 = \frac{ 36 \sqrt{3}}{2} + 18 \cdot l $$$$ 2 \cdot 229.2 = 36 \sqrt{ 3 } + 2 \cdot 18 \cdot l $$$$ 458.4 = 36 \sqrt{ 3 } + 36 \cdot l $$$$ 36 \cdot l = 458.4 - 36 \sqrt{ 3 } $$$$ l = \frac{ 458.4 - 36 \sqrt{ 3 } }{ 36 }$$$$ l = \frac{ 396.0462 }{ 36 }$$$$ l = 11.0013 $$

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