STEP 1: find height $ h $
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 16 $ and $ s = 17 $ we have:
$$ h ^ {\,2} + \frac{ 16^2 }{ 4 } = 17^2 $$ $$ h ^ {\,2} + \frac{ 256 }{ 4 } = 17^2 $$ $$ h ^ {\,2} + 64 = 17^2 $$ $$ h ^ {\,2} = 289 - 64 $$ $$ h ^ {\,2} = 225 $$ $$ h = \sqrt{ 225 } $$$$ h = 15 $$STEP 2: find volume $ V $
To find volume $ V $ use formula:
$$ V = \dfrac{ a ^{ 2 } \cdot h }{ 3 } $$After substituting $ a = 16 $ and $ h = 15 $ we have:
$$ V = \dfrac{ 256 \cdot 15 }{ 3 }$$$$ V = \dfrac{ 3840 }{ 3 } $$$$ V = 1280 $$