Find the side $ a $ of an equilateral triangle if area $A = \frac{\sqrt{ 3 }}{ 2 }$.
Answer
$a = \sqrt{ 2 }$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$After substituting $ A = \frac{\sqrt{ 3 }}{ 2 } $ we have:
$$ \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ \frac{\sqrt{ 3 }}{ 2 } \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 2 \sqrt{ 3 } = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 2 \sqrt{ 3 } }{ \sqrt{ 3 } } $$ $$ a^2 = 2 $$ $$ a = \sqrt{ 2 } $$This page was created using
Equilateral Triangle Calculator