Find the area $ A $ of a hexagon if long diagonal $d = 30$.
Answer
$A = \frac{ 675 \sqrt{ 3}}{ 2 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = 2 \cdot a $$After substituting $ d = 30 $ we have:
$$ 30 = 2 \cdot a $$ $$ a = \dfrac{ 30 }{ 2 } $$ $$ a = 15 $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 } $$After substituting $ a = 15 $ we have:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot 15^2 }{ 2 } $$ $$ A = \dfrac{ 3 \sqrt{ 3 } \cdot 225 }{ 2 }$$ $$ A = \dfrac{ 675 \sqrt{ 3 } }{ 2 }$$ $$ A = \frac{ 675 \sqrt{ 3}}{ 2 } $$This page was created using
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