STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $h = 4\, \text{cm}$ we have:

$$ 4\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 4\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 8\, \text{cm} $$ $$ a = \dfrac{ 8\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = \frac{ 8 \sqrt{ 3}}{ 3 }\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

$$ A = \frac{ a^2 \sqrt{3}}{2} + 3 a l $$

After substituting $a = \dfrac{ 8 \sqrt{ 3}}{ 3 }\, \text{cm}$ and $l = 15\, \text{cm}$ we have:

$$ A = \frac{ \frac{ 8 \sqrt{ 3}}{ 3 }\, \text{cm}^2 \sqrt{3}}{2} + 3 \cdot \frac{ 8 \sqrt{ 3}}{ 3 }\, \text{cm} \cdot 15\, \text{cm} $$$$ A = \frac{ \frac{ 64 }{ 3 }\, \text{cm}^2 \sqrt{3}}{2} + 3 \cdot 40 \sqrt{ 3 }\, \text{cm}^2 $$$$ A = \frac{ \frac{ 64 \sqrt{ 3}}{ 3 }\, \text{cm}^2}{2} + 120 \sqrt{ 3 }\, \text{cm}^2 $$$$ A = \frac{ 32 \sqrt{ 3}}{ 3 }\, \text{cm}^2 + 120 \sqrt{ 3 }\, \text{cm}^2 $$$$ A = \frac{ 392 \sqrt{ 3}}{ 3 }\, \text{cm}^2 $$

Triangular Prism Calculator