Find the area $ A $ of a triangular prism if length $l = 10$ and height $h = 3$.

$A = 66 \sqrt{ 3 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ h = 3 $ we have:

$$ 3 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 3 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 6 $$ $$ a = \dfrac{ 6 }{ \sqrt{ 3 } } $$ $$ a = 2 \sqrt{ 3 } $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ a = 2 \sqrt{ 3 } $ and $ l = 10 $ we have:

$$ A = \frac{ 2 \sqrt{ 3 }^2 \sqrt{3}}{2} + 3 \cdot 2 \sqrt{ 3 } \cdot 10 $$$$ A = \frac{ 12 \sqrt{3}}{2} + 3 \cdot 20 \sqrt{ 3 } $$$$ A = \frac{ 12 \sqrt{ 3 }}{2} + 60 \sqrt{ 3 } $$$$ A = 6 \sqrt{ 3 } + 60 \sqrt{ 3 } $$$$ A = 66 \sqrt{ 3 } $$

Triangular Prism Calculator