Find the perimeter $ P $ of a hexagon if incircle radius $r = 10$.
Answer
$P = 40 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ r = 10 $ we have:
$$ 10 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 10 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 20 $$ $$ a = \dfrac{ 20 }{ \sqrt{ 3 } } $$ $$ a = \frac{ 20 \sqrt{ 3}}{ 3 } $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 6 \cdot a $$After substituting $ a = \frac{ 20 \sqrt{ 3}}{ 3 } $ we have:
$$ P = 6 \cdot \frac{ 20 \sqrt{ 3}}{ 3 } $$ $$ P = 40 \sqrt{ 3 } $$This page was created using
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