STEP 1: find side $ a $

To find side $ a $ use formula:

After substituting $B = 169\, \text{cm}$ we have:

$$ B = a^2 $$ $$ a^2 = 169\, \text{cm} $$ $$ a = \sqrt{ 169\, \text{cm} } $$ $$ a = 13 $$

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$

After substituting $a = 13\, \text{cm}^0$ and $s = 9.7\, \text{cm}$ we have:

$$ h ^ {\,2} + \frac{ 13 }{ 4 } = \left( 9.7\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 169 }{ 4 } = \left( 9.7\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 169 }{ 4 } = \left( 9.7\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 94.09\, \text{cm}^2 - \frac{ 169 }{ 4 } $$ $$ h ^ {\,2} = 51.84\, \text{cm}^2 $$ $$ h = \sqrt{ 51.84\, \text{cm}^2 } $$$$ h = 7.2\, \text{cm} $$

STEP 3: find volume $ V $

To find volume $ V $ use formula:

$$ V = \dfrac{ a ^{ 2 } \cdot h }{ 3 } $$

After substituting $a = 13\, \text{cm}^0$ and $h = 7.2\, \text{cm}$ we have:

$$ V = \dfrac{ 169 \cdot 7.2\, \text{cm} }{ 3 }$$$$ V = \dfrac{ 1216.8\, \text{cm} }{ 3 } $$$$ V = 405.6\, \text{cm} $$

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