STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $V = 224\, \text{cm}$ and $l = 16\, \text{cm}$ we have:

$$ 224\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 16\, \text{cm} \right)^{4} }{ 4 } $$$$ 224\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 16\, \text{cm} \right)^{4} $$$$ 896\, \text{cm} = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 16\, \text{cm} \right)^{4} $$$$ 896\, \text{cm} = 16 \sqrt{ 3 }\, \text{cm} \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 896\, \text{cm}}{ 16 \sqrt{ 3 }\, \text{cm} } $$$$ a ^{ 2 } \approx 10.2914 $$$$ a \approx \sqrt{ 10.2914 } $$$$ a \approx 3.208 $$

STEP 2: find base area $ B $

To find base area $ B $ use formula:

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

After substituting $a = 3.208\, \text{cm}^0$ we have:

$$ B = \dfrac{ \sqrt{ 3 } \cdot 3.208 }{ 4 } $$ $$ B = \dfrac{ \sqrt{ 3 } \cdot 10.2914 }{ 4 }$$ $$ B = \dfrac{ 17.8253 }{ 4 }$$ $$ B = 4.4563 $$

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