Find the area $ A $ of a hexagon if perimeter $P = 14$.

$A = \frac{ 49 \sqrt{ 3}}{ 6 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

$$ P = 6 \cdot a $$

After substituting $ P = 14 $ we have:

$$ 14 = 6 \cdot a $$ $$ a = \dfrac{ 14 }{ 6 } $$ $$ a = \frac{ 7 }{ 3 } $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ a = \frac{ 7 }{ 3 } $ we have:

$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot \left(\frac{ 7 }{ 3 }\right)^2 }{ 2 } $$ $$ A = \dfrac{ 3 \sqrt{ 3 } \cdot \frac{ 49 }{ 9 } }{ 2 }$$ $$ A = \dfrac{ \frac{ 49 \sqrt{ 3}}{ 3 } }{ 2 }$$ $$ A = \frac{ 49 \sqrt{ 3}}{ 6 } $$

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