STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $h = 8\, \text{cm}$ we have:

$$ 8\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 8\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 16\, \text{cm} $$ $$ a = \dfrac{ 16\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = \frac{ 16 \sqrt{ 3}}{ 3 }\, \text{cm} $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

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

After substituting $a = \dfrac{ 16 \sqrt{ 3}}{ 3 }\, \text{cm}$ and $l = 13\, \text{cm}$ we have:

$$ V =\dfrac{ \sqrt{ 3 } \cdot \frac{ 16 \sqrt{ 3}}{ 3 }\, \text{cm} ^{ 2 } \cdot 13\, \text{cm} }{ 4 } $$$$ V = \dfrac{ \frac{ 256 \sqrt{ 3}}{ 3 }\, \text{cm}^2 \cdot 13\, \text{cm} }{ 4 }$$$$ V = \dfrac{ \frac{ 3328 \sqrt{ 3}}{ 3 }\, \text{cm}^3 }{ 4 } $$$$ V = \frac{ 832 \sqrt{ 3}}{ 3 }\, \text{cm}^3 $$

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