Find the volume $ V $ of a pyramid if slant height $s = 9.7$ and base area $B = 169$.

$V = 405.6$

STEP 1: find side $ a $

To find side $ a $ use formula:

After substituting $ B = 169 $ we have:

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

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

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

After substituting $ a = 13 $ and $ s = 9.7 $ we have:

$$ h ^ {\,2} + \frac{ 13^2 }{ 4 } = 9.7^2 $$ $$ h ^ {\,2} + \frac{ 169 }{ 4 } = 9.7^2 $$ $$ h ^ {\,2} + \frac{ 169 }{ 4 } = 9.7^2 $$ $$ h ^ {\,2} = 94.09 - \frac{ 169 }{ 4 } $$ $$ h ^ {\,2} = 51.84 $$ $$ h = \sqrt{ 51.84 } $$$$ h = 7.2 $$

STEP 3: find volume $ V $

To find volume $ V $ use formula:

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

After substituting $ a = 13 $ and $ h = 7.2 $ we have:

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

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