STEP 1: find side $ a $

To find side $ a $ use formula:

$$ AL = 3 \cdot a \cdot l $$

After substituting $AL = 360\, \text{cm}$ and $l = 12\, \text{cm}$ we have:

$$ 360\, \text{cm} = 3 \cdot a \cdot \left( 12\, \text{cm} \right)^{4} $$$$ 360\, \text{cm} = 36\, \text{cm} \cdot a $$$$ a = \dfrac{ 360\, \text{cm}}{ 36\, \text{cm} } $$$$ a \approx 3.1831 $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $a = 3.1831\, \text{cm}^0$ we have:

$$ h = \dfrac{ \sqrt{ 3 } \cdot 3.1831 }{ 2 } $$$$ h = \dfrac{ 5.5133 }{ 2 } $$ $$ h \approx 2.7566 $$

Triangular Prism Calculator