Find the area $ A $ of an equilateral triangle if incircle radius $r = 17$.

$A = 867 \sqrt{ 3 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$

After substituting $ r = 17 $ we have:

$$ 17 = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$ $$ \sqrt{ 3 } \cdot a = 17 \cdot 6 $$ $$ \sqrt{ 3 } \cdot a = 102 $$ $$ a = \dfrac{ 102 }{ \sqrt{ 3 } } $$ $$ a = 34 \sqrt{ 3 } $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ a = 34 \sqrt{ 3 } $ we have:

$$ A = \dfrac{ \sqrt{ 3 } \cdot \left(34 \sqrt{ 3 }\right)^2 }{ 4 } $$ $$ A = \dfrac{ \sqrt{ 3 } \cdot 3468 }{ 4 }$$ $$ A = \dfrac{ 3468 \sqrt{ 3 } }{ 4 }$$ $$ A = 867 \sqrt{ 3 } $$

Equilateral Triangle Calculator