Find the area $ A $ of a triangular prism if length $l = 15$ and height $h = 20$.

$A = \frac{ 2600 \sqrt{ 3}}{ 3 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ h = 20 $ we have:

$$ 20 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 20 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 40 $$ $$ a = \dfrac{ 40 }{ \sqrt{ 3 } } $$ $$ a = \frac{ 40 \sqrt{ 3}}{ 3 } $$

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{ 40 \sqrt{ 3}}{ 3 } $ and $ l = 15 $ we have:

$$ A = \frac{ \frac{ 40 \sqrt{ 3}}{ 3 }^2 \sqrt{3}}{2} + 3 \cdot \frac{ 40 \sqrt{ 3}}{ 3 } \cdot 15 $$$$ A = \frac{ \frac{ 1600 }{ 3 } \sqrt{3}}{2} + 3 \cdot 200 \sqrt{ 3 } $$$$ A = \frac{ \frac{ 1600 \sqrt{ 3}}{ 3 }}{2} + 600 \sqrt{ 3 } $$$$ A = \frac{ 800 \sqrt{ 3}}{ 3 } + 600 \sqrt{ 3 } $$$$ A = \frac{ 2600 \sqrt{ 3}}{ 3 } $$

Triangular Prism Calculator