Find the area $ A $ of a triangular prism if length $l = 12$ and height $h = 7.8$.

$A = 394.4919$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ h = 7.8 $ we have:

$$ 7.8 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 7.8 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 15.6 $$ $$ a = \dfrac{ 15.6 }{ \sqrt{ 3 } } $$ $$ a \approx 9.0067 $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ a = 9.0067 $ and $ l = 12 $ we have:

$$ A = \frac{ 9.0067^2 \sqrt{3}}{2} + 3 \cdot 9.0067 \cdot 12 $$$$ A = \frac{ 81.12 \sqrt{3}}{2} + 3 \cdot 108.08 $$$$ A = \frac{ 140.504}{2} + 324.2399 $$$$ A = 70.252 + 324.2399 $$$$ A = 394.4919 $$

Triangular Prism Calculator