STEP 1: find side $ a $

To find side $ a $ use formula:

$$ V = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot l }{ 4 } $$

After substituting $V = 4495.4\, \text{cm}$ and $l = 19\, \text{cm}$ we have:

$$ 4495.4\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 19\, \text{cm} \right)^{4} }{ 4 } $$$$ 4495.4\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 19\, \text{cm} \right)^{4} $$$$ 17981.6\, \text{cm} = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 19\, \text{cm} \right)^{4} $$$$ 17981.6\, \text{cm} = 19 \sqrt{ 3 }\, \text{cm} \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 17981.6\, \text{cm}}{ 19 \sqrt{ 3 }\, \text{cm} } $$$$ a ^{ 2 } \approx 173.9255 $$$$ a \approx \sqrt{ 173.9255 } $$$$ a \approx 13.1881 $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $a = 13.1881\, \text{cm}^0$ and $l = 19\, \text{cm}$ we have:

$$ A = \frac{ 13.1881^2 \sqrt{3}}{2} + 3 \cdot 13.1881 \cdot 19\, \text{cm} $$$$ A = \frac{ 173.9255 \sqrt{3}}{2} + 3 \cdot 250.5735\, \text{cm} $$$$ A = \frac{ 301.2478}{2} + 751.7206\, \text{cm} $$$$ A = 150.6239 + 751.7206\, \text{cm} $$$$ A = 902.3445 $$

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