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