Find the area $ A $ of a triangular prism if length $l = 15$ and height $h = 4$.

$A = \frac{ 392 \sqrt{ 3}}{ 3 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ h = 4 $ we have:

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

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ a = \frac{ 8 \sqrt{ 3}}{ 3 } $ and $ l = 15 $ we have:

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

Triangular Prism Calculator