Find the side $ a $ of a triangular prism if length $l = 20$ and area $A = 108$.
Answer
$a = 0.333$
Explanation
To find side $ a $ use formula:
$$ A = \frac{ a^2 \sqrt{3}}{2} + 3 a l $$After substituting $ A = 108 $ and $ l = 20 $ we have:
$$ 108 = \frac{ a^2 \sqrt{3}}{2} + 3 \cdot a \cdot 20 $$$$ 216 = a^2 \sqrt{3} + 648 \cdot a $$$$ a^2 \sqrt{3} + 648 \cdot a - 216 = 0 $$( use quadratic equation solver to solve this quadratic equation )
$$ a = 0.333 $$This page was created using
Triangular Prism Calculator