STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $V = 4.5\, \text{cm}$ and $l = 3\, \text{cm}$ we have:

$$ 4.5\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 3\, \text{cm} \right)^{4} }{ 4 } $$$$ 4.5\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 3\, \text{cm} \right)^{4} $$$$ 18\, \text{cm} = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 3\, \text{cm} \right)^{4} $$$$ 18\, \text{cm} = 3 \sqrt{ 3 }\, \text{cm} \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 18\, \text{cm}}{ 3 \sqrt{ 3 }\, \text{cm} } $$$$ a ^{ 2 } \approx 1.1027 $$$$ a \approx \sqrt{ 1.1027 } $$$$ a \approx 1.0501 $$

STEP 2: find height $ h $

To find height $ h $ use formula:

$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$

After substituting $a = 1.0501\, \text{cm}^0$ we have:

$$ h = \dfrac{ \sqrt{ 3 } \cdot 1.0501 }{ 2 } $$$$ h = \dfrac{ 1.8188 }{ 2 } $$ $$ h \approx 0.9094 $$

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