Find the area $ A $ of a triangular prism if length $l = 3$ and height $h = 1.6$.

$A = 19.5837$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ h = 1.6 $ we have:

$$ 1.6 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 1.6 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 3.2 $$ $$ a = \dfrac{ 3.2 }{ \sqrt{ 3 } } $$ $$ a \approx 1.8475 $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ a = 1.8475 $ and $ l = 3 $ we have:

$$ A = \frac{ 1.8475^2 \sqrt{3}}{2} + 3 \cdot 1.8475 \cdot 3 $$$$ A = \frac{ 3.4133 \sqrt{3}}{2} + 3 \cdot 5.5426 $$$$ A = \frac{ 5.9121}{2} + 16.6277 $$$$ A = 2.956 + 16.6277 $$$$ A = 19.5837 $$

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