STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $h = 2\, \text{cm}$ we have:

$$ 2\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 2\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 4\, \text{cm} $$ $$ a = \dfrac{ 4\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = \frac{ 4 \sqrt{ 3}}{ 3 }\, \text{cm} $$

STEP 2: find lateral $ AL $

To find lateral $ AL $ use formula:

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

After substituting $a = \dfrac{ 4 \sqrt{ 3}}{ 3 }\, \text{cm}$ and $l = 13\, \text{cm}$ we have:

$$ AL = 4 \sqrt{ 3 }\, \text{cm} \cdot 13\, \text{cm} $$$$ AL = 52 \sqrt{ 3 }\, \text{cm}^2 $$

Triangular Prism Calculator