Find the area $ A $ of an equilateral triangle if perimeter $P = 24$.
Answer
$A = 16 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ P = 3 \cdot a $$After substituting $ P = 24 $ we have:
$$ 24 = 3 \cdot a $$ $$ a = \dfrac{ 24 }{ 3 } $$ $$ a = 8 $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 } $$After substituting $ a = 8 $ we have:
$$ A = \dfrac{ \sqrt{ 3 } \cdot 8^2 }{ 4 } $$ $$ A = \dfrac{ \sqrt{ 3 } \cdot 64 }{ 4 }$$ $$ A = \dfrac{ 64 \sqrt{ 3 } }{ 4 }$$ $$ A = 16 \sqrt{ 3 } $$This page was created using
Equilateral Triangle Calculator