Find the height $ h $ of a triangular prism if volume $V = 4.8$ and base area $B = 7.2$.

$h = 3.5314$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ B = 7.2 $ we have:

$$ 7.2 = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 7.2 \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 28.8 = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 28.8 }{ \sqrt{ 3 } } $$ $$ a^2 = 16.6277 $$ $$ a = \sqrt{ 16.6277 } $$$$ a \approx 4.0777 $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $ a = 4.0777 $ we have:

$$ h = \dfrac{ \sqrt{ 3 } \cdot 4.0777 }{ 2 } $$$$ h = \dfrac{ 7.0628 }{ 2 } $$ $$ h \approx 3.5314 $$

Triangular Prism Calculator