Find the area $ A $ of an equilateral triangle if perimeter $P = 24 \sqrt{ 3 }$.

$A = 48 \sqrt{ 3 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

$$ P = 3 \cdot a $$

After substituting $ P = 24 \sqrt{ 3 } $ we have:

$$ 24 \sqrt{ 3 } = 3 \cdot a $$ $$ a = \dfrac{ 24 \sqrt{ 3 } }{ 3 } $$ $$ a = 8 \sqrt{ 3 } $$

STEP 2: find area $ A $

To find area $ A $ use formula:

$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 } $$

After substituting $ a = 8 \sqrt{ 3 } $ we have:

$$ A = \dfrac{ \sqrt{ 3 } \cdot \left(8 \sqrt{ 3 }\right)^2 }{ 4 } $$ $$ A = \dfrac{ \sqrt{ 3 } \cdot 192 }{ 4 }$$ $$ A = \dfrac{ 192 \sqrt{ 3 } }{ 4 }$$ $$ A = 48 \sqrt{ 3 } $$

Equilateral Triangle Calculator