Find the height $ h $ of a triangular prism if length $l = 9$ and base area $B = 10$.

$h = 4.1618$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ B = 10 $ we have:

$$ 10 = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 10 \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 40 = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 40 }{ \sqrt{ 3 } } $$ $$ a^2 = \frac{ 40 \sqrt{ 3}}{ 3 } $$ $$ a = \sqrt{ \frac{ 40 \sqrt{ 3}}{ 3 } } $$$$ a \approx 4.8056 $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $ a = 4.8056 $ we have:

$$ h = \dfrac{ \sqrt{ 3 } \cdot 4.8056 }{ 2 } $$$$ h = \dfrac{ 8.3236 }{ 2 } $$ $$ h \approx 4.1618 $$

Triangular Prism Calculator