Find the area $ A $ of a square if circumcircle radius $R = 8$.
Answer
$A = 128$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ R = \dfrac{ \sqrt{ 2 } \cdot a }{ 2 } $$After substituting $ R = 8 $ we have:
$$ 8 = \dfrac{ \sqrt{ 2 } \cdot a }{ 2 } $$ $$ \sqrt{ 2 } \cdot a = 8 \cdot 2 $$ $$ \sqrt{ 2 } \cdot a = 16 $$ $$ a = \dfrac{ 16 }{ \sqrt{ 2 } } $$ $$ a = 8 \sqrt{ 2 } $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = a^2 $$After substituting $ a = 8 \sqrt{ 2 } $ we have:
$$ A = \left(8 \sqrt{ 2 }\right)^2 $$ $$ A = 128 $$This page was created using
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