Find the volume $ V $ of a pyramid if side $a = 40$ and slant height $s = 29$.

$V = 11200$

STEP 1: find height $ h $

To find height $ h $ use Pythagorean Theorem:

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

After substituting $ a = 40 $ and $ s = 29 $ we have:

$$ h ^ {\,2} + \frac{ 40^2 }{ 4 } = 29^2 $$ $$ h ^ {\,2} + \frac{ 1600 }{ 4 } = 29^2 $$ $$ h ^ {\,2} + 400 = 29^2 $$ $$ h ^ {\,2} = 841 - 400 $$ $$ h ^ {\,2} = 441 $$ $$ h = \sqrt{ 441 } $$$$ h = 21 $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

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

After substituting $ a = 40 $ and $ h = 21 $ we have:

$$ V = \dfrac{ 1600 \cdot 21 }{ 3 }$$$$ V = \dfrac{ 33600 }{ 3 } $$$$ V = 11200 $$

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