Find the height $ h $ of a triangular prism if volume $V = 1500$ and base area $B = 250$.

$h = 20.809$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ B = 250 $ we have:

$$ 250 = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 250 \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 1000 = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 1000 }{ \sqrt{ 3 } } $$ $$ a^2 = \frac{ 1000 \sqrt{ 3}}{ 3 } $$ $$ a = \sqrt{ \frac{ 1000 \sqrt{ 3}}{ 3 } } $$$$ a \approx 24.0281 $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $ a = 24.0281 $ we have:

$$ h = \dfrac{ \sqrt{ 3 } \cdot 24.0281 }{ 2 } $$$$ h = \dfrac{ 41.6179 }{ 2 } $$ $$ h \approx 20.809 $$

Triangular Prism Calculator